Finite-time stability for Markovian jump nonlinear systems with random delays

This paper investigates the stochastic finite-time stability (SFTS) problem for a class of Markovian jump nonlinear systems with time delays. The nonlinear terms are assumed to satisfy the Lipschitz conditions, and the time delays are modelled by mutually independent stochastic variables subject to Bernoulli distributions. The aim of our work is to design a set of linear feedback controllers such that the addressed system is SFTS in the presence of Markov jumps, random delays, and nonlinearity. In our work, first the SFTS performances are analyzed by virtue of Lyapunov functional and stochastic control strategy. Then according to these analyses, new criterion are given in terms of linear matrix inequalities (LMIs) in order to design the feedback controller. In addition, a reasonable strategy is proposed to reduce the resource consumption of controller design. And the effect of random delays on control performances is also discussed. Finally, an illustrative example is provided to validate the proposed method.