Stability analysis of systems with multiple nonlinearities

This paper shows a method for using describing functions in a control system with multiple nonlinearities. The linear system resulting after the proper describing functions have been inserted is analyzed using an "input dependent root locus" which is a modified root locus technique. The rules for construction of the input dependent locus and a proof of its applicability are given along with examples which illustrate the method. The technique shows the existence of limit cycles, their amplitude and frequency when they exist, and the stability of the limit cycle.