Lecture 1 - Introduction
Lecture 2 - First Order systems
Lecture 3 - Classification of Equilibrium points
Lecture 4 - Lipschitz Functions
Lecture 5 - Existence/uniqueness theorems
Lecture 6 - Existence/uniqueness of solutions to differential equations
Lecture 7 - Lyapunov theorem on stability
Lecture 8 - Extension of Lyapunov's Theorem in different contexts
Lecture 9 - LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbits
Lecture 10 - Bendixson criterion and Poincare-Bendixson criterion. Example: Lotka Volterra predator prey model
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 Review of linearization, operating point/operating trajectory
Lecture 13 - Signals, 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 & non-linearity, 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 tranformations and circle criterion
Lecture 22 - Nonlinearities based on circle criterion
Lecture 23 - Limit cycles
Lecture 24 - Popov criterion continuous, frequency-domain theorem
Lecture 25 - Popov criterion continuous, frequency-domain theorem
Lecture 26 - Describing function method
Lecture 27 - Describing Function : 2
Lecture 28 - Describing : optimal gain
Lecture 29 - Describing : optimal gain
Lecture 30 - Describing functions : Jump Hysteresis
Lecture 31 - Describing functions : sufficient conditions for existence of periodic orbits non 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
