Limit Cycles and Stability Criteria

Chapter 2 of the book Nonlinear Systems and Controls deals with the stability theory of dynamic systems. At the beginning, the determination of limit cycles is explained using the method of description functions. The concept of absolute stability, the Popov criterion, the Tsypkin criterion, and the circle criterion are described; followed by Lyapunov's stability theory. The chapter concludes with the theory of passive systems and dissipative Hamiltonian systems. Real-world examples, including an underwater glider and a self balancing vehicle, accompany the description of the theory, along with various exercises.