Finite-time Stabilization for Singular Markov Jump Systems with Generally Uncertain Transition Rates

This paper studies the problem of finite-time stabilization for singular Markov jump systems (SMJSs) with time-varying delays and generally uncertain transition rates. First, a suitable Lyapunov-Krasovskii functional is constructed. And the criterion of the finite-time stability for singular Markov jump systems is analyzed. We adopt a better design approach for the matrix P over bar i\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{P}}_i$$\end{document} satisfying the equality constraints, which is much less conservative. Then, a state feedback controller design method based on linear matrix inequalities (LMIs) is presented to ensure that the closed-loop system is finite-time stable. Finally, simulation examples are given to illustrate the results' correctness and validity of this paper.