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

Abstract

In this technical brief, delaydependent nonfragile Hâˆ‍ control problem of a class of stochastic nonlinear systems with interval timevarying statedelays has been considered using Lyapunov–Krasovskii (LK) functional approach. By exploiting a candidate LK functional and using freeweighting matrix technique, a less conservative delaydependent stabilization criterion is presented for the existence of a nonfragile memoryless statefeedback controller, which ensures stochastic stability as well as a prescribed Hâˆ‍ performance level of the closedloop 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.