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Lecture 30 of 35Nonlinear Dynamical Systems

L30-Describing function : Jump Hysteresis

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

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Nonlinear Dynamical Systems, IIT Bombay (at NPTEL)
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All the lectures

  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