Introduction – First Order systems – Classification of Equilibrium points – Lipschitz Functions – Existence uniqueness theorems – Existence uniqueness of solutions to differential equations – Lyapunov theorem on stability – Extension of Lyapunov’s Theorem in different contexts – LaSalle’s Invariance principle, Barbashin and Krasovski theorems, periodic orbits – Bendixson criterion and Poincare-Bendixson criterion.Ex:Lotka Volterra predator prey – Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator – Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator – Signals, operators – Norms of signals, systems (operators), Finite gain L2 stable – Nyquist plots and Nyquist criterion for stability – Interconnection between linear system & non-linearity, passive filters – Passive filters, Dissipation equality, positive real lemma – Positive real lemma proof – Definition for positive realness and Kalman Yakubovich-Popov Theorem – Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities

Loop tranformations and circle criterion – Nonlinearities based on circle criterion – Limit cycles – Popov criterion continuous, frequency-domain theorem – Describing function method – Describing Function – Describing : optimal gain – Describing function : Jump Hysteresis – Describing functions:sufficient conditions for existence of periodic orbits – Describing functions for nonlinearities – Ideal relay with Hysteresis and dead zone – Dynamical systems on manifolds

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Course Curriculum

Introduction Details 47:51
First Order systems Details 51:22
Classification of Equilibrium points Details 52:53
Lipschitz Functions Details 55:18
Existence uniqueness theorems Details 53:4
Existence uniqueness of solutions to differential equations I Details 41:49
Lyapunov theorem on stability Details 54:35
Extension of Lyapunov’s Theorem in different contexts Details 55:56
LaSalle’s Invariance principle, Barbashin and Krasovski theorems, periodic orbits Details 54:59
Bendixson criterion and Poincare-Bendixson criterion.Ex:Lotka Volterra predator prey Details 57:22
Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator II Details 36:32
Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator Details 42:43
Signals, operators Details 56:18
Norms of signals, systems (operators), Finite gain L2 stable Details 52:19
Nyquist plots and Nyquist criterion for stability Details 50:41
Interconnection between linear system & non-linearity, passive filters Details 52:13
Passive filters, Dissipation equality, positive real lemma Details 47:38
Positive real lemma proof I Details 52:28
Definition for positive realness and Kalman Yakubovich-Popov Theorem Details 51:43
Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities Details 54:30
Loop tranformations and circle criterion Details 49:23
Nonlinearities based on circle criterion Details 56:26
Limit cycles Details 50:13
Popov criterion continuous, frequency-domain theorem Details 50:9
Popov criterion continuous, frequency-domain theorem I Details 51:3
Describing function method Details 1:2:40
Describing Function I Details 58:6
Describing : optimal gain II Details 50:34
Describing : optimal gain III Details 59:25
Describing function : Jump Hysteresis IV Details 58:47
Describing functions:sufficient conditions for existence of periodic orbits V Details 52:34
Describing functions for nonlinearities VI Details 49:21
Ideal relay with Hysteresis and dead zone Details 52:28
Dynamical systems on manifolds-1 Details 53:15
Dynamical systems on manifolds I Details 42:48

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