LMI approach to suboptimal guaranteed cost control for uncertain time-delay systems

Results on the design of robust memoryless slate feedback controllers for u ncertain time-delay systems with norm bounded uncertainty are presented. It is proved that the feasibility of a linear matrix inequality (LMI) problem is necessary and sufficient for the quadratic stabilisation of an uncertai n time-delay system. A robust state feedback controller can be constructed using the corresponding feasible solution of the LMI problem. A procedure i s given to select a suitable state feedback controller that is also subopti mal in the sense of minimising a bound on a quadratic performance index.