Necessary and sufficient criteria for asynchronous stabilization of Markovian jump systems

摘要

This paper is concerned with asynchronous stabilization for a class of discrete-time Markovian jump systems. The mode of designed controller is considered to be not perfectly synchronous with the activated mode of the Markovian jump system. In order to achieve the asymptotic stability with asynchronous controller, a conditional probability is introduced to describe the asynchronism of system and controller modes, which is dependent on the active system mode. Besides, due to the difficulty in acquiring all the mode transition probabilities in practice, the transition probabilities of the Markovian jump system and the controllers are supposed to be partially unknown. A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities. Finally, the effectiveness and advantages of the proposed methods are demonstrated by two illustrative examples. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.