Disturbance-observer-based control for non-homogeneous semi-Markov jump systems with time-varying delays.

This paper discusses the issue of disturbance-observer-based control (DOBC) for a kind of continuous-time non-homogeneous semi-Markov jump systems (SMJSs) with time-varying delays. Unlike the existing results, the system examined in this article is about non-homogeneous SMJSs, which indicates that its transition rates (TRs) is time-varying. The versions of TRs matrices are selected by a switching signal, which is independent of the semi-Markov process that decides on the system modes. The time-varying TRs are established to be of two situations: stochastic process and arbitrary switching, respectively. First, we construct a novel class of Lyapunov function that is related to both system mode and switching signal mode, thus it can make more use of information about the system and help reduce conservatism. Second, some conditions are given to guarantee the exponentially mean square stable of the SMJSs and H ∞ output tracking performance index. Finally, two examples are provided to demonstrate the efficacy of research methods. [ABSTRACT FROM AUTHOR]