Restricted Stabilization of Markovian Jump Systems Based on a Period and Random Switching Controller

Abstract

This paper considers the stabilization of continuous-time Markovian jump systems (MJSs) via a restricted controller. It is actually a period and random switching controller. It also contains some existing controllers as special ones. Sufficient conditions for existence of such a controller are established by studying a discrete-time MJS, which are presented in terms of LMIs and depend on its period and probability. Moreover, an extension about a similar but aperiodic controller is considered. Finally, a numerical example is used to demonstrate the effectiveness and superiority of the proposed methods. INDEX TERMS Markovian jump systems; stabilization; period and random switching; semi-Markov process; linear matrix inequalities (LMIs)

Design of sliding mode fault‐tolerant control for Markovian jump systems with probabilistic delay: A discrete partitioning strategy

“…The key feature of MJSs lies in the switching between multiple modes via a given Markov chain, which is much different from single dynamic systems. Accordingly, many interesting methods have been proposed for MJSs according to specific requirements, such as a restricted controller‐based stabilization scheme in Reference 4. To conserve network resources, an event‐driven rule has been introduced into the design process of the control scheme, and two kinds of observer‐based/state‐feedback event‐triggered schemes have already been designed in Reference 5 for the purpose of transferring the system data intermittently.…”