Stability analysis of pulsewidth-modulated feedback systems

We present new Lyapunov and Lagrange stability results for pulse-width-modulated (PWM) feedback systems with linear plants. We consider the non-critical 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 while 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 stability results. We employ quadratic Lyapunov functions in our analysis. However, in the proofs we make use of different majorizations, requiring hypotheses that differ significantly from those used in the existing results. Additionally, we incorporate into our results optimization procedures that improve our results significantly. We demonstrate the applicability and quality of our results by means of two specific examples that are identical to examples presented in the literature