Stabilization of delayed Markovian jump systems with sampled controllers

Abstract

This paper mainly studies the stabilization problem of continuous-time delayed Markovian jump systems by a sampled controller. Not only the state is sampled, but also the switching signals, where the latter sampled signal makes the synthesis and analysis of delayed systems more complex and difficult. To address these issues, this paper develops an augmented system approach, resulting in a novel system model that incorporates two delayed exponential matrices. It has been demonstrated that the stability properties of original delayed system can be ensured by the constructed auxiliary system. The correlation among Markov process, sampling interval and time delay is first established, and several stabilization results are given. More special situations about the proposed sampled are further considered. The validity and superiority of the method proposed in this paper are verified through two numerical examples.