H∞ control of a class of piecewise homogeneous Markov jump linear systems

In this paper, the problem of H_infin control for a class of Markov jump linear system (MJLS) with timevarying transition rates (TRs) is investigated. The time-varying character of TRs is considered as finite piecewise homogeneous and the variations of TR matrices in the finite set are considered as two types: arbitrary variation and stochastic variation. The latter means that the variations are subject to a higher-level transition rate matrix. The mode-dependent and variation-dependent Lyapunov function evaluated for the system energy is constructed, and the appropriate evolvement of the Lyapunov function is explored for both categories of variations such that the stability and performance analysis of the closed-loop system can be carried out. Then, the H_infin controllers in an adaptation sense are designed ensuring that the resulting closed-loop systems are stochastically stable and have a guaranteed H_infin noise-attenuation performance index. A numerical example is provided to verify the theoretical results.