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source: nptelhrd 2014年12月15日

Electrical - Nonlinear Dynamical Systems by Prof. Harish K. Pillai and Prof. Madhu N.Belur, Department of Electrical Engineering, IIT Bombay. For more details on NPTEL visit http://nptel.ac.in

01 Introduction 47:51

02 First Order systems 51:22

03 Classification of Equilibrium points 52:53

04 Lipschitz Functions 55:18

05 Existence uniqueness theorems 53:04

06 Existence uniqueness of solutions to differential equations 41:49

07 Lyapunov theorem on stability 54:35

08 Extension of Lyapunov's Theorem in different contexts 55:56

09 LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbits 54:59

10 Bendixson criterion and Poincare-Bendixson criterion.Ex:Lotka Volterra predator prey 57:22

11 Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator 36:32

12 Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator 42:43

13 Signals, operators 56:18

14 Norms of signals, systems (operators), Finite gain L2 stable 52:19

15 Nyquist plots and Nyquist criterion for stability 50:41

16 Interconnection between linear system & non-linearity, passive filters 52:13

17 Passive filters, Dissipation equality, positive real lemma 47:38

18 Positive real lemma proof 52:28

19 Definition for positive realness and Kalman Yakubovich-Popov Theorem 51:43

20 Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities 54:30

21 Loop transformations and circle criterion 49:23

22 Nonlinearities based on circle criterion 56:26

23 Limit cycles 50:13

24 Popov criterion continuous, frequency-domain theorem 50:09

25 Popov criterion continuous, frequency-domain theorem 51:03

26 Describing function method 1:02:40

27 Describing Function :2 58:06

28 Describing : optimal gain 50:34

29 Describing : optimal gain 59:25

30 Describing function : Jump Hysteresis 58:47

31 Describing functions:sufficient conditions for existence of periodic orbits 52:34

32 Describing functions for nonlinearities 49:21

33 Ideal relay with Hysteresis and dead zone 52:28

34 Dynamical systems on manifolds-1 53:15

35 Dynamical systems on manifolds-2 42:48

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