Finite-time stabilization for nonlinear discrete-time singular Markov jump systems with piecewise-constant transition probabilities subject to average dwell time

Abstract

In this paper, the finite-time boundedness and stabilization issues for nonlinear discrete-time singular Markov jump systems with time-varying transition probabilities subject to average dwell time switching are studied for the first time. The finite piecewise homogeneous character of transition probabilities is taken into account. Firstly, by using average dwell time approach and implicit function theorem, a sufficient condition is presented such that the nonlinear discrete-time singular Markov jump systems are singular finite-time bounded and of a unique solution. Secondly, according to the singular value decomposition approach, a linear matrix inequality (LMI) finite-time boundedness criterion is developed, which can be used for constructing state feedback controllers directly. Based on this LMI finite-time boundedness criterion, the state feedback controller design is handled. Finally, three numerical examples are presented to illustrate the validity and advantage of the proposed methods.