Nonlinear Dynamical Systems by Harish K. Pillai & Madhu N. Belur (IIT Bombay)

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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