ABSTRACT
This chapter begins with a classical graphical idea of looking at the solutions on a graph. It demonstrates that the existence of multiple equilibrium points and of limit cycles in the case of nonlinear systems. The chapter presents some useful classical theorems for the prediction of limit cycles in second-order systems. An in-depth and general approach for the stability analysis of nonlinear control systems is the theory dating back to the late nineteenth century and contributed by the Russian mathematician Lyapunov. The chapter addresses the problem of finding Lyapunov functions for general, nonlinear systems. The forward path is a linear time-invariant system, and the feedback part is a memoryless nonlinearity, i.e. a nonlinear static mapping. For some nonlinear systems, with a few reasonable assumptions, the frequency response method, called the describing function method, can be used to approximately analyze and predict nonlinear behavior. The main purpose of this technique is for the prediction of limit cycles in nonlinear systems.
