Electrical - Nonlinear Dynamical Systems (English)

   Thursday, May 01, 2025   

Starting a new Lecture Notes Series on Electrical - Nonlinear Dynamical Systems

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Electrical - Nonlinear Dynamical Systems By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction

Lecture 2: Mod-01 Lec-02 First Order systems

Lecture 3: Mod-01 Lec-03 Classification of Equilibrium points

Lecture 4: Mod-01 Lec-04 Lipschitz Functions

Lecture 5: Mod-01 Lec-05 Existence uniqueness theorems

Lecture 6: Mod-01 Lec-06 Existence uniqueness of solutions to differential equations

Lecture 7: Mod-01 Lec-07 Lyapunov theorem on stability

Lecture 8: Mod-01 Lec-08 Extension of Lyapunov's Theorem in different contexts

Lecture 9: Mod-01 Lec-09 LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbits

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

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

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

Lecture 13: Mod-01 Lec-13 Signals, operators

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

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

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

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

Lecture 18: Mod-01 Lec-18 Positive real lemma proof

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

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

Lecture 21: Mod-01 Lec-21 Loop tranformations and circle criterion

Lecture 22: Mod-01 Lec-22 Nonlinearities based on circle criterion

Lecture 23: Mod-01 Lec-23 Limit cycles

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

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

Lecture 26: Mod-01 Lec-26 Describing function method

Lecture 27: Mod-01 Lec-27 Describing Function :2

Lecture 28: Mod-01 Lec-28 Describing : optimal gain

Lecture 29: Mod-01 Lec-29 Describing : optimal gain

Lecture 30: Mod-01 Lec-30 Describing function : Jump Hysteresis

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

Lecture 32: Mod-01 Lec-32 Describing functions for nonlinearities

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

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

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