Pth Moment Exponential Stability Of Stochastic PWM Feedback Systems

Pulse-width-modulation has extensively been used in many areas.There has beena growing research interest on the stability analysis for PWM feedback systems, and aset of stability results have been established by a variety of methods. There are, however,only few (if any) results concerning the qualitative properties of stochasticpulse-width-modulation systems, especially the stability analysis of stochastic PWMsystems with time varying delays. On the other hand, in the actual process, randomfactors and time delay will inevitably occur in electronic neural networks owing to theunavoidable finite switching speed of amplifiers, we found that the time delay, externalrandom disturbance and parameter uncertainty are important factors instability andoscillatory response of networks, so the parameter uncertain stochastic neural networkstability is particularly important.To the best of the authors’ knowledge, this paper further studies Momentexponential stability of the critical case of PWM feedback systems with stochasticperturbations and the moment exponential stability of pulse-width-modulated (PWM)feedback system with time varying which is subjected to multiplicative and additiverandom disturbance modeled by the derivative of Wiener process. Obviously, based onthe pulse-width-modulation feedback system uniqueness, such systems are somewhatcomplex in comparison with most of the systems in literature. By choosing reasonableLyapunov-Krasovskii functional, combined with linear matrix inequalities andIto integration method, we shall establish several Lyapunov and Lagrange criteria for pthmoment exponential stability in mean, and then present an algorithm to compute theupper bound for the parameters of PWM. We shall characterize the relationship amongthe parameters of pulse-width-modulation, time varying delays and the coefficient ofstate vectors of the feedback systems. It will be shown that when the randomdisturbance is sufficiently small such PWM feedback system is globally exponentiallystable in mean provided that the upper bounds of parameters of pulse-width-modulatorare selected properly. We also demonstrate the effectiveness of our results by means ofseveral numerical examples.