LMI approach to optimal guaranteed cost control for a class of linear uncertain discrete systems

The problem of guaranteed cost control for a class of linear discrete uncertain system is considered. The system under consideration contains convex polyhedral uncertain parameters. An upper bound of the performance measured by standard quadratic function is constructed, and a method of designing state feedback robust stabilizing control law guaranteeing this quadratic performance index of system to be less than this upper bound is derived. It is proved that whether such a control law exists is equivalent to the feasibility of a group of linear matrix inequality. Also, a procedure is given to select an optimal state feedback controller in the sense of minimizing the upper bound of quadratic performance index