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Course10810100235 lectures

Nonlinear Dynamical Systems

Prof. Harish K. Pillai and Prof. Madhu N.Belur · IIT Bombay

Start with lecture 1 At NPTEL

Lectures

Nonlinear Dynamical Systems

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

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Bombay
Department
Electrical Engineering
Taught by
Prof. Harish K. Pillai, Prof. Madhu N.Belur
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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