Stabilization of Discrete-Time Systems via a Partially Disabled Controller Experiencing Forced Dwell Times

Abstract

This paper focuses on the stabilization problem of discrete-time systems via exploiting a partially disabled controller, where a stochastic variable with two values is used to describe a controller useful or not. Particularly, the adopted stochastic variable is not the traditional Bernoulli variable, but a variable has forced dwell times on the basis of traditional Bernoulli variable. Due to such a stochastic variable included, two kinds of dwell times, named as fixed and random dwell times, respectively are included in the closed-loop system. It will be shown that the stochastic stability of the original closed-loop system could be guaranteed by the established auxiliary system with state jumps. More importantly, sufficient conditions for the existence of the desired controller are presented with linear matrix inequalities forms. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.