ABSTRACT
This chapter discusses the problem of non-fragile guaranteed cost control for discrete-time linear systems under state feedback controller gain uncertainties. It is well known that even small perturbations in controller parameters could destabilize the closed-loop system. The state feedback control designs for optimal guaranteed cost control under the classes of gain uncertainties are given in terms of solutions to algebraic Riccati equations. The designs are such that the cost of the closed-loop system is guaranteed to be within a certain bound for all admissible uncertainties. For additive controller gain uncertainties, an optimal guaranteed cost control design is presented in terms of an algebraic Riccati equation, which corresponds to the standard optimal control design for the same system with a modified cost function. Under a bound condition for the gain uncertainties, an optimal guaranteed cost control design is given for the case of the multiplicative gain uncertainties.
