Finite-time stability of uncertain Markovian jump systems with time-varying and distributed delays

This paper is concerned with the analysis of robust stochastic finite-time stability of Markovian jump systems with parameter uncertainties, time-varying and distributed delays. It is assumed that the parameter uncertainties are norm bounded and the time-varying delays are mode-dependent. By constructing a suitable stochastic Lyapunov functional and employing genearlized Itô´s formula and Gronwall inequality, a delay- and mode-dependent condition is established to guarantee stochastic finite-time stability of nominal Markovian jump systems. Then, by robust control technique, a stochastic finite-time stability criterion is obtained for the uncertain case. These conditions can be verified efficiently in practice. Finally, two numerical examples are explored to illustrate the effectiveness of the developed results.