Finite-Time Annular Domain Stability and Asynchronous Control for Stochastic Switching Markov Jump Systems
Weihai Zhang, Shiyu Zhong, Xiushan Jiang
Abstract
This paper mainly investigates the stochastic finite-time annular domain stability and asynchronous <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for nonlinear stochastic switching Markov jump systems. Firstly, the criterion of stochastic finite-time annular domain stability of the system is given by the modedependent average dwell time method, and two results, which consider particular cases with no switching signal and no Markov jump, are obtained. Secondly, when there are asynchronous phenomena in both deterministic switching and Markov jump, the asynchronous <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller is given to make the nonlinear switching Markov jump system 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 switching Markov jump systems is obtained. Finally, an example is given to illustrate the results.