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 L-2 - L-infinity 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 L-2 - L-infinity 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. (C) 2016 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.