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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 11 - Bendixson and Poincare-Bendixson Criteria, van der Pol Oscillator

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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 Poincare-Bendixson Criterion

Lecture 11 - Bendixson and Poincare-Bendixson Criteria, van der Pol Oscillator

Lecture 12 - Scilab Simulation of Lotka-Volterra 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 Kalman-Yakubovich-Popov Theorem

Lecture 20 - Kalman-Yakubovich-Popov 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