Non-fragile Generalized H2 Control for Linear Time-Delay Systems

This paper is concerned with problem of non-fragile generalized H₂ control for linear time-delay systems. The state feedback gains are with norm-bounded controller uncertainties. For both the cases with additive and multiplicative controller uncertainties, it is addressed to design memoryless state feedback controllers such that, for all admissible uncertainties, the resulting closed-loop system is stable and has the given generalized H₂ level. Sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the expected memoryless state feedback controllers can be easily constructed via convex optimization. The result provided in this paper can be extended to dealing with uncertain time-delay systems. An illustrative example is given to demonstrate the validity and applicability of the proposed approach.