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)
Lecture 19 - Definition for Positive Realness and Kalman-Yakubovich-Popov Theorem