Robust linear controller under state and control constraints

The linear robust constrained regulation problem is investigated. It is shown that the theory of polyhedral positively invariant sets can provide simple solutions to both the analysis and the synthesis of linear constrained regulators for systems with parameter uncertainties. For both problems, a solution can be obtained by applying simple linear programming algorithms. An optimization method is established for the determination of linear state feedback control laws which transfer asymptotically to the origin any initial state belonging to a prespecified convex set, while linear constraints on the control vector are satisfied for any perturbed system.<>