Nonlinear Dynamical Systems
Nonlinear Dynamical Systems. Instructors: Prof. Madhu N. Belur and Prof. Harish K. Pillai, Department of Electrical Engineering, IIT Bombay. This course covers basics of nonlinear differential equations that are encountered when dealing with practical dynamical systems in the context of their control. Topics covered include: introduction to nonlinear dynamical systems' features, existence and uniqueness of solutions, Lipschitz condition, linearization and local analysis, classification of equilibrium points (planar case), periodic orbits, Lyapunov theory, Lure problem, sector nonlinearity, Nyquist criterion, Lp stability, small gain theorem, passivity result, circle/Popov criteria, and describing function method.
(from nptel.ac.in)
Lecture 01  Introduction 
Lecture 02  First Order Systems 
Lecture 03  Classification of Equilibrium Points 
Lecture 04  Lipschitz Functions 
Lecture 05  Existence and Uniqueness Theorems 
Lecture 06  Existence and Uniqueness of Solutions to Differential Equations 
Lecture 07  Lyapunov Theorem on Stability 
Lecture 08  Extension of Lyapunov Theorem in Different Contexts 
Lecture 09  LaSalle's Invariance Principle, Barbashin and Krasovski Theorems, Periodic Orbits 
Lecture 10  Bendixson Criterion and PoincareBendixson Criterion 
Lecture 11  Bendixson and PoincareBendixson Criteria, van der Pol Oscillator 
Lecture 12  Scilab Simulation of LotkaVolterra Predator Prey Model, van der Pol Oscillator 
Lecture 13  Signals and Norms of Operators 
Lecture 14  Norms of Signals, Systems (Operators), Finite Gain L2 Stable 
Lecture 15  Nyquist Plots and Nyquist Criterion for Stability 
Lecture 16  Interconnection between Linear System and Nonlinearity, Passive Filters 
Lecture 17  Passive Filters, Dissipation Equality, Positive Real Lemma 
Lecture 18  Positive Real Lemma Proof 
Lecture 19  Definition for Positive Realness and KalmanYakubovichPopov Theorem 
Lecture 20  KalmanYakubovichPopov Lemma/Theorem and Memoryless Nonlinearities 
Lecture 21  Loop Transformations and Circle Criterion 
Lecture 22  Nonlinearities based on Circle Criterion 
Lecture 23  Limit Cycles 
Lecture 24  Popov Criterion, Frequency Domain Theorem 
Lecture 25  Popov Criterion, Frequency Domain Theorem 
Lecture 26  Describing Function Method 
Lecture 27  Describing Function 
Lecture 28  Describing Functions: Optimal Gain 
Lecture 29  Describing Functions: Optimal Gain (cont.) 
Lecture 30  Describing Functions: Jump Hysteresis 
Lecture 31  Describing Functions: Sufficient Conditions for Existence of Periodic Orbits 
Lecture 32  Describing Functions for Nonlinearities 
Lecture 33  Ideal Relay with Hysteresis and Dead Zone 
Lecture 34  Dynamical Systems on Manifolds 1 
Lecture 35  Dynamical Systems on Manifolds 2 
References 
Nonlinear Dynamical Systems
Instructors: Prof. Madhu N. Belur and Prof. Harish K. Pillai, Department of Electrical Engineering, IIT Bombay. This course covers basics of nonlinear differential equations that are encountered when dealing with practical dynamical systems in the context of their control.
