Constrained feedback control of discrete-time systems decribed by ARMA models

In this paper the problem of determination of bounded output-feedback control laws which stabilize multivariable discrete-time systems described by ARMA models is investigated. The proposed approach is based upon the properties of polyhedral positively invariant sets with respect to this class of systems. In the first part of the paper, necessary and sufficient conditions for the positive invariance of polyhedral sets are established. Then, conditions guaranteeing the existence of a solution to the constrained control problem are developed. Finally, it is shown that a solution to this problem can been obtained by solving a linear programming problem.