Optimal guaranteed cost control for a class of linear uncertain time-delay systems

This paper studies the optimal guaranteed control problem for a class of linear uncertain time-delay systems. The systems under consideration are described by state differential equations with time-varying unknown but norm-bounded uncertain parameters and time-varying unknown but bounded delay in states. An upper bound of the performance measured by standard quadratic function is constructed and based an the delay-depended stabilizing approach, a method of designing state feedback robust quadratic stabilizing control law guaranteeing this quadratic performance index be less than the constructed upper bound is derived. A procedure is given to select an optimal state feedback controller in the sense of minimizing this upper bound of quadratic performance index. The results depend on the sue of delay and are given in terms of several linear matrix inequalities (LMIs).