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September 25, 2023

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Description

Nonlinear Dynamical Systems. Instructors: Prof. Madhu N. Belur and Prof. Harish K. Pillai, Department of Electrical Engineering, IIT Bombay.

This course covers basics of nonlinear differential equations that are encountered when dealing with practical dynamical systems in the context of their control. Topics covered include: introduction to nonlinear dynamical systems' features, existence and uniqueness of solutions, Lipschitz condition, linearization and local analysis, classification of equilibrium points (planar case), periodic orbits, Lyapunov theory, Lure problem, sector nonlinearity, Nyquist criterion, Lp stability, small gain theorem, passivity result, circle/Popov criteria, and describing function method. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Introduction Unlimited
  • Lecture 02 – First Order Systems Unlimited
  • Lecture 03 – Classification of Equilibrium Points Unlimited
  • Lecture 04 – Lipschitz Functions Unlimited
  • Lecture 05 – Existence and Uniqueness Theorems Unlimited
  • Lecture 06 – Existence and Uniqueness of Solutions to Differential Equations Unlimited
  • Lecture 07 – Lyapunov Theorem on Stability Unlimited
  • Lecture 08 – Extension of Lyapunov Theorem in Different Contexts Unlimited
  • Lecture 09 – LaSalle’s Invariance Principle, Barbashin and Krasovski Theorems, Periodic Orbits Unlimited
  • Lecture 10 – Bendixson Criterion and Poincare-Bendixson Criterion Unlimited
  • Lecture 11 – Bendixson and Poincare-Bendixson Criteria, van der Pol Oscillator Unlimited
  • Lecture 12 – Scilab Simulation of Lotka-Volterra Predator Prey Model, van der Pol Oscillator Unlimited
  • Lecture 13 – Signals and Norms of Operators Unlimited
  • Lecture 14 – Norms of Signals, Systems (Operators), Finite Gain L2 Stable Unlimited
  • Lecture 15 – Nyquist Plots and Nyquist Criterion for Stability Unlimited
  • Lecture 16 – Interconnection between Linear System and Nonlinearity, Passive Filters Unlimited
  • Lecture 17 – Passive Filters, Dissipation Equality, Positive Real Lemma Unlimited
  • Lecture 18 – Positive Real Lemma Proof Unlimited
  • Lecture 19 – Definition for Positive Realness and Kalman-Yakubovich-Popov Theorem Unlimited
  • Lecture 20 – Kalman-Yakubovich-Popov Lemma/Theorem and Memoryless Nonlinearities Unlimited
  • Lecture 21 – Loop Transformations and Circle Criterion Unlimited
  • Lecture 22 – Nonlinearities based on Circle Criterion Unlimited
  • Lecture 23 – Limit Cycles Unlimited
  • Lecture 24 – Popov Criterion, Frequency Domain Theorem Unlimited
  • Lecture 25 – Popov Criterion, Frequency Domain Theorem Unlimited
  • Lecture 26 – Describing Function Method Unlimited
  • Lecture 27 – Describing Function Unlimited
  • Lecture 28 – Describing Functions: Optimal Gain Unlimited
  • Lecture 29 – Describing Functions: Optimal Gain (cont.) Unlimited
  • Lecture 30 – Describing Functions: Jump Hysteresis Unlimited
  • Lecture 31 – Describing Functions: Sufficient Conditions for Existence of Periodic Orbits Unlimited
  • Lecture 32 – Describing Functions for Nonlinearities Unlimited
  • Lecture 33 – Ideal Relay with Hysteresis and Dead Zone Unlimited
  • Lecture 34 – Dynamical Systems on Manifolds 1 Unlimited
  • Lecture 35 – Dynamical Systems on Manifolds 2 Unlimited

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