A novel approach to the computation of the maximal controlled invariant set for constrained linear systems

In this paper, the problem of the determination of the maximal controlled invariant set of linear systems subject to polyhedral input and state constraints, together with the corresponding state-feedback control law is investigated. Instead of computing one-step reachable sets or maximizing the volume of a specific invariant set, the proposed method consists of the iterative expansion of an initial “small” invariant set by adding new vertices to its convex hull. This is achieved by minimizing the distance of each new vertex from the vertices of the polyhedral set defining the state constraints. This approach, established for both continuous-time and discrete-time systems, does not require invertibility of matrix A, open-loop stability or symmetry of the constraints.