Finite-Time Annular Domain Stability and Asynchronous $H_{\infty }$ Control for Stochastic Switching Markov Jump Systems

This article mainly investigates the stochastic finite-time annular domain stability (SFTADS) and asynchronous
$H_{\infty }$
control for nonlinear stochastic switching Markov jump systems (SMJSs). First, the criterion of SFTADS of the system is given by the mode-dependent average dwell time method, and two results, which consider particular cases with no switching signal and no Markov jump, are obtained. Second, when there are asynchronous phenomena in both deterministic switching and Markov jump, the asynchronous
$H_{\infty }$
controller is given to make the nonlinear SMJS finite-time annular domain bounded with a prescribed disturbance attenuation level. In addition, two degradation results with no deterministic asynchrony and no stochastic asynchrony are derived, respectively. As a special case, the corresponding result of linear SMJSs is obtained. Finally, an example is given to illustrate the results.