LMI Approach to Robust Delay-Dependent Mixed H2/H∞ Controller of Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays

The design of a robust mixed H2/H∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H2/H∞ controller minimizes an upper bound of the H2 performance measure, while guaranteeing an H∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H2/H∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H2/H∞ controller achieving the minimization of an upper bound of the closed-loop H2 performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method.