Nonlinear Dynamical Systems Video Lectures

Nonlinear Dynamical Systems
'Nonlinear Dynamical Systems' Video Lectures by Prof. Harish K. Pillai, Prof. Madhu N.Belur from IIT Bombay
"Nonlinear Dynamical Systems" - Video Lectures
1. L1-Introduction
2. L2-First Order systems
3. L3-Classification of Equilibrium points
4. L4-Lipschitz Functions
5. L5-Existence/uniqueness theorems
6. L6-Existence/uniqueness of solutions to differential equations
7. L7-Lyapunov theorem on stability
8. L8-Extension of Lyapunov's Theorem in different contexts
9. L9-LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbits
10. L10-Bendixson criterion and Poincare-Bendixson criterion. Example: Lotka Volterra predator prey model
11. L11-Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator
12. L12-Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator Review of linearization, operating point/ operating trajectory
13. L13-Signals, operators
14. L14-Norms of signals, systems (operators), Finite gain L2 stable
15. L15-Nyquist plots and Nyquist criterion for stability
16. L16-Interconnection between linear system & non-linearity, passive filters
17. L17-Passive filters, Dissipation equality, positive real lemma
18. L18-Positive real lemma proof
19. L19- Definition for positive realness and Kalman Yakubovich-Popov Theorem
20. L20-Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities
21. L21-Loop tranformations and circle criterion
22. L22-Nonlinearities based on circle criterion
23. L23-Limit cycles
24. L24-Popov criterion continuous, frequency-domain theorem
25. L25-Popov criterion continuous, frequency-domain theorem
26. L26-Describing function method
27. L27-Describing Function :2
28. L28-Describing : optimal gain
29. L29-Describing : optimal gain
30. L30-Describing function : Jump Hysteresis
31. L31-Describing functions : sufficient conditions for existence of periodic orbits non existence of periodic orbits
32. L32-Describing functions for nonlinearities
33. L33-Ideal relay with Hysteresis and dead zone
34. L34-Dynamical systems on manifolds-1
35. L35-Dynamical systems on manifolds-2
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