Hidden Markov model‐based asynchronous exponential stabilization for stochastic Markovian jump systems with incomplete controller mode information

Abstract

In this paper, the exponential stability of a kind of It Markovian jump system is studied. Specifically, the exponential stability is ensured by designing an asynchronous delayed‐feedback controller, whose modes are inconsistent with those of the original system. We have built the necessary new relationship between controller modes and system modes, which can facilitate the stability analysis and also make the famous existing ones special cases of the proposed one. Moreover, practically ubiquitous controller delays, which occur between the sensors and controllers, to the detriment of the system stability, are taken into account, and their maximum values are provided in a theoretic way. In this way, the exponential stability can be well ensured against controller delays. With an eye to practical applications, the transition rates of the considered system and the designed asynchronous controller are assumed to be uncertain, and they can be well dealt with by using a new approach with lower conservatism. Furthermore, a practical example and some comparative examples are given to demonstrate the effectiveness and superiorities of the obtained conclusion.