Time/Event-Triggered Exponential Stabilization for Stochastic Systems: Enhancing Nonlinearity Tolerance

Abstract

This article seeks the enhancement of nonlinearity tolerance in time/event-triggered stabilization for stochastic systems. In the related results, the controller functions are required to obey global Lipschitz condition for the suppression of sampling/execution error, and the drift and/or diffusion coefficients of the stochastic systems are restricted to polynomial or, even, linear growth. These limitations deserve overcoming for enlarged applications. To this end, a distinct framework of time/event-triggered controls is established for stochastic systems, targeted at exponential stabilization. Specifically, inclusive Lyapunov-type feasibility conditions are proposed by capturing the effect of sampling/execution error and distinguishing the role of system nonlinearities. Particularly, different from the related results, the evolution of sampling/execution error is subtly exploited via Lyapunov functions to reveal the dynamic interaction between the sampling/execution errors and system state. Then, time-triggered exponential stabilization via sampled-data controller is achieved not only in the moment sense but also in the almost sure sense. Accordingly, Lyapunov function based analysis is performed for the composite dynamics of system state and sampling error, confronted with the coupling of discontinuous and stochastic features. To further reduce execution, periodic event-triggered control is exploited to achieve exponential stabilization for stochastic nonlinear systems, by virtue of the relation with the dynamic evolution under sampled-data control. Through typical examples, we demonstrate the potential of our framework in handling the cases with the controller functions violating global Lipschitz condition and with the system nonlinearities beyond polynomial growth.