Robust synthesis of constrained linear state feedback using LMIs and polyhedral invariant sets

This paper deals with the synthesis of linear feedback controllers for constrained discrete-time linear systems with polytopic uncertainty description. This problem was initially tackled using ellipsoidal robust invariant sets in the paper by Kothare (Kothare et al., Automatica, 1996) leading to an LMI-based optimization problem. The contribution of this paper is twofold. First the aforementioned method is extended to also take into account mixed state/input constraints and cross-terms between states and inputs in the objective function. Secondly, polyhedral invariant sets (Pluymers et al., ACC, 2005) are introduced in the synthesis algorithm in order to eliminate conservative constraint handling. This results in a provably more optimal feedback controller. The resulting method can either be used on-line in a receding horizon fashion to obtain a robust constrained controller or off-line in order to obtain a feedback controller with a guaranteed feasible region for use in dual-mode or other robust model-based predictive control algorithms. A numerical example is given to illustrate the new algorithm.