Feedback control of linear discrete-time systems under state and control constraints

In this paper the problem of stabilizing linear discrete-time systems under state and control linear constraints is studied. Based on the concept of positive invariance, existence conditions of linear state feedback control laws respecting both the constraints are established. These conditions are then translated into an algorithm of linear programming. 1. Introduction Most industrial systems must operate within fixed bounds and are subject to strict control limitations. The determination of closed-loop controls for such systems by state or output feedback often reduces to solving an associated unconstrained problem and then modifying the solution by superimposition of state and control limitations. The global stability of these control schemes is usually not guaranteed. Another approach that is more rigorous, consists of explicitly introducing the constraints in the lagrangian formulation of an optimal control problem (Mouradi 1979, Franckena and Sivan 1979, Gauthier and Bornard 1983). However, its implementation is not simple, because as an open-loop scheme it implies considerable off-line computation and as a closed-loop scheme it is represented by a non-linear controller. The concept of invariance (or positive invariance), which is related to the notion of Lyapunov functions, is a convenient tool both for guaranteeing stability and