Delay-variation-dependent stability for Markovian jump systems with time-varying delay and partial information on transition probabilities

The delay-variation-dependent robust stability problem is investigated for uncertain Markovian jump systems (UMJSs) with time-varying delay and partial information on transition probabilities. The time-varying delay and its time variation respectively, are assumed to belong to respective bounded intervals. An augmented Lyapunov-Krasovskii functional (LKF) is constructed by introducing a newly delay decomposition method. Also, some novel sufficient criteria are derived to guarantee MJSs to be robustly asymptotically stable in the mean square for all admissible uncertainties by combing the Wirtinger integral inequality and the reciprocally convex technique. All the stability criteria are formulated in the form of linear matrix inequalities (LMIs), which are fully dependent upon the bounds of the time-varying delay and its time variation. Some numerical examples are given to show the effectiveness and less conservatism of the proposed method.