H2 guaranteed cost control for uncertain discrete-time systems under state and control constraints

This paper deals with the H₂ guaranteed cost control problem for uncertain discrete-time linear systems subject to both polyhedral state and control constraints. The convex-bounded parametric uncertainties are studied. Based on the theory of ellipsoidal positively invariant sets, a sufficient condition is obtained for determining a quadratic stabilizing state-feedback gain and an H₂-norm upper bound which hold for all feasible models. A programming approach is proposed which solves at each step a convex optimization problem involving linear matrix inequalities