Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities

This paper investigates the robust reliable control problem for a class of nonlinear time-delay stochastic systems. The system under study involves stochastics, state time-delay, parameter uncertainties, possible actuator failures and unknown nonlinear disturbances, which are often encountered in practice and the sources of instability. Our attention is focused on the design of linear state feedback memoryless controllers such that, for all admissible uncertainties as well as actuator failures occurring among a prespecified subset of actuators, the plant remains stochastically exponentially stable in mean square, independent of the time delay. Sufficient conditions are proposed to guarantee the desired robust reliable exponential stability despite possible actuator failures, which are in terms of the solutions to algebraic Riccati inequalities. An illustrative example is exploited to demonstrate the applicability of the proposed design approach.