Stability analysis of pulse-width-modulated feedback systems

In this paper, we present new Lyapunov and Lagrange stability results for p ulse-width-modulated (PWM) feedback systems with linear and nonlinear plant s. For systems with linear plants, we consider the noncritical case, where the poles of the transfer function of the plant are all in the left-half of the complex plane and the critical case, where one pole is at the origin w hile the remaining poles are all in the left-half of the complex plane. For these systems we apply the Direct Method of Lyapunov to establish new and improved results for both Lyapunov and Lagrange stability. As in most exist ing results for PWM feedback systems obtained by the Lyapunov method, we em ploy quadratic Lyapunov functions in our analysis. However, in the proofs w e make use of different majorizations, requiring hypotheses that differ sig nificantly from those used in the existing results. Additionally, and perha ps more importantly, we incorporate into our results optimization procedure s that improve our results significantly. We demonstrate the applicability and quality of our results by means of five specific examples that are iden tical to examples presented in the literature. For PWM feedback systems wit h nonlinear plants we show that under reasonable conditions. the stability properties of the trivial solution of such systems can be deduced from the stability properties of the trivial solution of PWM feedback systems with c orresponding linearized plant, for both noncritical and critical cases. (C) 2001 Published by Elsevier Science Ltd.