ℋ2 guaranteed cost control for uncertain discrete-time linear systems

The ℋ 2 guaranteed cost control problem is analysed for uncertain, discrete-time linear systems. It consists on the determination of a constant state feedback stabilizing matrix gain and an ℋ 2 -norm upper bound which holds for all feasible models. Two different approaches are considered. The first is based on the optimality conditions provided by Bellmans's dynamic programming equation. The second is based on the geometric properties of the aforementioned problem. It is shown that it is possible to parametrize all stabilizing gains over a convex set. In this special parameter space, the ℋ 2 cost is found to be a linear function of the free parameters. Finally, some relationships between these approaches are presented and numerical examples given.