# Nonlinear Dynamical Systems

IIT Bombay, , Prof. Harish K. Pillai

IIT Bombay, , Prof. Harish K. Pillai

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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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 httpnptel.ac.in

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.