Control of uncertain discrete-time systems with guaranteed cost

This paper is concerned with the problem of LQR design for uncertain discrete-time systems. The system under consideration has time-varying norm-bounded parameter uncertainties in both the state and input matrices. The problem addressed is the design of a state feedback control law such that the cost of the system is guaranteed to be within a certain bound for all admissible uncertainties, which is referred to as `guaranteed cost control.´ It is shown that the optimal guaranteed cost control is related to a recursive Riccati difference equation for the finite horizon case and to a `game type´ discrete-time Riccati equation for the infinite horizon case