Robust Nonfragile Stabilizing Controller for an Uncertain Stochastic Nonlinear System With Interval Time-Varying State-Delays: Prescribed H_∞ Performance Level

In this technical brief, delay-dependent nonfragile H_∞ control problem of a class of stochastic nonlinear systems with interval time-varying state-delays has been considered using Lyapunov–Krasovskii (LK) functional approach. By exploiting a candidate LK functional and using free-weighting matrix technique, a less conservative delay-dependent stabilization criterion is presented for the existence of a nonfragile memoryless state-feedback controller, which ensures stochastic stability as well as a prescribed H_∞ performance level of the closed-loop system in the presence admissible parametric uncertainties in the system as well as in the controller gains and exogenous input signal. Since the resulting stabilization criterion is in terms of nonlinear matrix inequalities (NLMIs), it is solved using cone complementarity algorithm (CCA) to obtain a stabilizing controller. A numerical example is presented to illustrate the effectiveness of the proposed result.