1 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

2 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

3 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

4 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

5 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

6 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

7 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 

8 
L6Existence/uniqueness of solutions to
differential equations 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

9 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

10 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

11 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

12 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

13 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

14 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

15 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

16 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Friday 


17 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Saturday 


18 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Monday 


19 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

20 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

21 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

22 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

23 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

24 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

25 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

26 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

27 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

28 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

29 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

30 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

31 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

32 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

33 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

34 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

35 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

36 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

37 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

38 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

39 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

40 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

41 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

42 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

43 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

44 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

45 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

46 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

47 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

48 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

49 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

50 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

51 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

52 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

53 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

54 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

55 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

56 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

57 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

58 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

59 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

60 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

61 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

62 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

63 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

64 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

65 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

66 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

67 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

68 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

69 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

70 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

71 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

72 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

73 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

74 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

75 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

76 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

77 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

78 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

79 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

80 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

81 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

82 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

83 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

84 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

85 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

86 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

87 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

88 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

89 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

90 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

91 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

92 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

93 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

94 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

95 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

96 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

97 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

98 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

99 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

100 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

101 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

102 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

103 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

104 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

105 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

106 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

107 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

108 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

109 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

110 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

111 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

112 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

113 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

114 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

115 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

116 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

117 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

118 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

119 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

120 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

121 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

122 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

123 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

124 
L1Introduction 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

125 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

126 
L1Introduction 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

127 
L1Introduction 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

128 
L2First Order systems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

129 
L2First Order systems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

130 
L2First Order systems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

131 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

132 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

133 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

134 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

135 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

136 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

137 
L5Existence/uniqueness theorems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

138 
L5Existence/uniqueness theorems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

139 
L5Existence/uniqueness theorems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

140 
L6Existence/uniqueness of solutions to
differential equations 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

141 
L6Existence/uniqueness of solutions to
differential equations 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

142 
L6Existence/uniqueness of solutions to
differential equations 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

143 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

144 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

145 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

146 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Thursday 


147 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Friday 


148 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Saturday 


149 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

150 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

151 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

152 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

153 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

154 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

155 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

156 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

157 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

158 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

159 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

160 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

161 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

162 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

163 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

164 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

165 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

166 
Norms of signals, systems (operators), Finite gain
L2 stable 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

167 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

168 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

169 
Nyquist plots and Nyquist criterion for stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

170 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

171 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

172 
Interconnection between linear system 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

173 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

174 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

175 
Passive filters, Dissipation equality, positive
real lemma 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

176 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

177 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

178 
Positive real lemma proof 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

179 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

180 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

181 
Definition for positive realness and Kalman
YakubovichPopov Theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

182 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

183 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

184 
KalmanYakubovichPopov Lemma_theorem and
memoryless nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

185 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

186 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

187 
Loop tranformations and circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

188 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

189 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

190 
Nonlinearities based on circle criterion 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

191 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

192 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

193 
Limit cycles 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

194 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

195 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

196 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

197 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

198 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

199 
Popov criterion continuous, frequencydomain
theorem 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

200 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

201 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

202 
Describing function method 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

203 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

204 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

205 
L27Describing Function :2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

206 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

207 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

208 
L28Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

209 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

210 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

211 
L29Describing : optimal gain 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

212 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

213 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

214 
L30Describing function : Jump Hysteresis 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

215 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

216 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

217 
L31Describing functions : sufficient conditions
for existence of periodic orbits non existence of
periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

218 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

219 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

220 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

221 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

222 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

223 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

224 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

225 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

226 
L32Describing functions for nonlinearities 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

227 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

228 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

229 
L33Ideal relay with Hysteresis and dead zone 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

230 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Monday 

231 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Tuesday 

232 
L34Dynamical systems on manifolds1 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

233 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Thursday 

234 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

235 
L35Dynamical systems on manifolds2 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Saturday 

236 
L1Introduction 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 

237 
L2First Order systems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

238 
L3Classification of Equilibrium points 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

239 
L4Lipschitz Functions 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 

240 
L5Existence/uniqueness theorems 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

241 
L6Existence/uniqueness of solutions to
differential equations 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

242 
L7Lyapunov theorem on stability 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 

243 
L8Extension of Lyapunov's Theorem in different
contexts 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 


Wednesday 


244 
L9LaSalle's Invariance principle, Barbashin and
Krasovski theorems, periodic orbits 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

245 
L10Bendixson criterion and PoincareBendixson
criterion. Example: Lotka Volterra predator prey
model 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 

246 
L11Bendixson and PoincareBendixson criteria
vanderPol Oscillator 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Wednesday 

247 
L12Scilab simulation of Lotka Volterra predator
prey model, vanderPol Oscillator Review of
linearization,operating point/ operating
trajectory 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Friday 

248 
L13Signals, operators 
Prof. Madhu N.Belur ,Prof. Harish K. Pillai , IIT Bombay 

Sunday 
