Optimal guaranteed cost control of linear uncertain systems with input constraints

The guaranteed cost control problem for a class of linear systems with norm-bounded time-varying parameter uncertainties and input constraints is considered. A sufficient condition for the existence of guaranteed cost state feedback controllers is derived in terms of the solvability to a certain system of linear matrix inequalities (LMIs), and the feasible solutions to the system of LMIs provide a parametrized representation of a set of guaranteed cost controllers. Furthermore, the characterization of guaranteed cost controllers is exploited to solve the optimal guaranteed cost control problem. An example is given to illustrate the effectiveness of the proposed results.