Finite-Time Stabilization of Markov Jump Systems via a Probabilistic Event-Triggered Strategy

This paper investigates the finite-time stabilization of a class of Markov jump systems (MJSs). To regulate the limited network resource, a probabilistic event-triggered mechanism (PETM) is initially proposed. Based on the output of PETM, mode-dependent state feedback controllers are designed to obtain the closed-loop system (CLS). A set of novel Lyapunov functional are created to analyze the finite-time stability of the CLS. Afterward, the design algorithm is established to calculate the controller gains. Finally, simulations are provided to verify the proposed results.

I. Introduction

Recently, Markov jump systems (MJSs) have received an ever-growing attention owing to the capability of modelling abrupt changes [1]–[6]. For instance, mismatched output feedback control of linear MJSs were investigated in [1] based on a hierarchical sensor failure model. Subject to the imperfect (partial or uncertain) transition probabilities, the state estimation and extended dissipative control issue were concentrated for MJSs in [2] and [3], respectively. H_∞ control of linear MJSs was tackled in [4] from the view point of finite-time frequency. In [5], [6], the authors focused on the probabilistic distribution of sojourn time and discussed a more general type of MJSs named semi-MJSs.