Optimal guaranteed cost control of a class of nonlinear uncertain discrete-time systems: an LMI approach

The optimal guaranteed cost control problem for a class of nonlinear uncertain discrete-time systems is considered. A sufficient condition for the existence of guaranteed cost state feedback control is presented, and the problem of designing the optimal guaranteed cost control is converted to a convex optimization problem subjected to a certain system of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed results