Non-fragile delay-dependent guaranteed cost control for uncertain systems with both discrete and distributed delays

This paper investigates the design of non-fragile delay-dependent guaranteed cost controller for uncertain systems with time-varying discrete and distributed delays. The state feedback gain is with norm-bounded controller uncertainty. Our attention is focused on the design of non- fragile state feedback controllers such that the resulting closed-loop system is robustly stable, and a specified linear quadratic cost function has an upper bound for all admissible uncertainties. A delay-dependent sufficient condition is developed with matrix inequalities. The cone complementary linearization (CCL) method is exploited to cast it into a minimization problem subject to LMI constraints, which can be readily solved using standard numerical algorithm. A numerical example is provided to illustrate the effectiveness of the proposed design methods.