In this paper, we present new Lyapunov and Lagrange stability results for pulse-width-modulated (PWM) feedback systems with linear and nonlinear plants. 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 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 results for both Lyapunov and Lagrange stability. As in most existing results for PWM feedback systems obtained by the Lyapunov method, 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, and perhaps more importantly, we incorporate into our results optimization procedures that improve our results significantly. We demonstrate the applicability and quality of our results by means of five specific examples that are identical to examples presented in the literature. For PWM feedback systems with 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 corresponding linearized plant, for both noncritical and critical cases.