Robust reliable control of uncertain nonlinear stochastic systems subject to actuator fault

Abstract

This paper addresses the issue of robust reliable stabilization for a class of uncertain nonlinear stochastic systems with both discrete and distributed time-varying delays and possible occurrence of actuator faults. By constructing a new Lyapunov functional and using linear matrix inequality technique, a new set of sufficient conditions is established for the stochastic stability of the uncertain nonlinear stochastic systems. Then, sufficient conditions are obtained for the solvability of the robust stabilization problem via robust reliable controller. More precisely, the derived control law guarantees the robust stabilization of nonlinear stochastic systems in the presence of known actuator failure matrix and uncertainties. Further, the results are extended to study the stabilization of stochastic systems with unknown actuator failure matrix. Moreover, the obtained criteria are formulated in terms of LMIs and also the reliable controller can be designed in terms of the solutions to certain linear matrix inequalities. Finally, numerical examples with simulation result are presented to demonstrate the validity and less conservatism of the obtained results.