Optimal guaranteed cost control for uncertain discrete-time linear systems (Q2726029)

The author considers the problem of designing an optimal guaranteed cost state feedback controller for a class of discrete-time linear systems with norm-bounded time-varying parameter uncertainty and a quadratic cost index. First, a necessary and sufficient condition for the existence of guaranteed cost controllers is derived. Furthermore, it is shown that this condition is equivalent to the solvability of a system of linear matrix inequalities, and a parametric representation of guaranteed cost controllers is provided. Based on that, the problem of designing the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Finally, an example is given to illustrate the proposed results.