Robust resilient L2−L∞ control for uncertain stochastic systems with multiple time delays via dynamic output feedback

This paper deals with the problem of robust resilient L2−L∞ control for stochastic systems with multiple time delays and norm-bounded parameter uncertainties via dynamic output feedback. Both additive and multiplicative controller gain perturbations are considered. New delay-dependent conditions of robust mean-square exponential stability are developed by applying the Lyapunov-Krasovskii functional method and introducing free-weighting matrices. Two lemmas are given for reducing high-order nonlinearities, with the aid of which sufficient conditions are presented for the solvability of the robust resilient L2−L∞ control problem. The desired controllers can be constructed through the numerical solutions of a set of linear matrix inequalities. The proposed design conditions can be employed to determine reduced-order dynamic output feedback controllers without the need to impose any extra constraints on the system parameters. Numerical examples are provided to illustrate the effectiveness of the obtained results.