Stabilization of stochastically singular nonlinear jump systems with unknown parameters and continuously distributed delays

摘要

In this paper, the problem of robustly asymptotic stabilization for a class of stochastically nonlinear singular jump systems is investigated. The jumping parameters are modeled as a continuous-time, finite-state Markov chain. Based on the Lyapunov-Krasovskii functional and stochastic analysis theory as well as a state feedback control technique, some new sufficient conditions are derived to ensure the asymptotic stability of the trivial solution in the mean square. A key feature of this paper is that singular, nonlinear, noise perturbations, unknown parameters and continuously distributed delays are all considered. In particular, the obtained stabilization criteria in this paper are expressed in terms of LMIs, which can be solved easily by recently developed algorithms. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results. Moreover, the second example shows that delay-dependent stabilization criteria are less conservative than delay-independent criteria.