Electrical – Nonlinear Dynamical Systems

Mod-01 Lec-01 Introduction

Mod-01 Lec-02 First Order systems

Mod-01 Lec-03 Classification of Equilibrium points

Mod-01 Lec-04 Lipschitz Functions

Mod-01 Lec-05 Existence uniqueness theorems

Mod-01 Lec-06 Existence uniqueness of solutions to differential equations

Mod-01 Lec-07 Lyapunov theorem on stability

Mod-01 Lec-08 Extension of Lyapunov’s Theorem in different contexts

Mod-01 Lec-09 LaSalle’s Invariance principle, Barbashin and Krasovski theorems, periodic orbits

Mod-01 Lec-10 Bendixson criterion and Poincare-Bendixson criterion.Ex:Lotka Volterra predator prey

Mod-01 Lec-11 Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator

Mod-01 Lec-12 Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator

Mod-01 Lec-13 Signals, operators

Mod-01 Lec-14 Norms of signals, systems (operators), Finite gain L2 stable

Mod-01 Lec-15 Nyquist plots and Nyquist criterion for stability

Mod-01 Lec-16 Interconnection between linear system & non-linearity, passive filters

Mod-01 Lec-17 Passive filters, Dissipation equality, positive real lemma

Mod-01 Lec-18 Positive real lemma proof

Mod-01 Lec-19 Definition for positive realness and Kalman Yakubovich-Popov Theorem

Mod-01 Lec-20 Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities

Mod-01 Lec-21 Loop tranformations and circle criterion

Mod-01 Lec-22 Nonlinearities based on circle criterion

Mod-01 Lec-23 Limit cycles

Mod-01 Lec-24 Popov criterion continuous, frequency-domain theorem

Mod-01 Lec-25 Popov criterion continuous, frequency-domain theorem

Mod-01 Lec-26 Describing function method

Mod-01 Lec-27 Describing Function :2

Mod-01 Lec-28 Describing : optimal gain

Mod-01 Lec-29 Describing : optimal gain

Mod-01 Lec-30 Describing function : Jump Hysteresis

Mod-01 Lec-31 Describing functions:sufficient conditions for existence of periodic orbits

Mod-01 Lec-32 Describing functions for nonlinearities

Mod-01 Lec-33 Ideal relay with Hysteresis and dead zone

Mod-01 Lec-34 Dynamical systems on manifolds-1

Mod-01 Lec-35 Dynamical systems on manifolds-2