Parametric time-optimal control of linear discrete-time systems by state feedback Part 2. Irregular Kronecker invariants

Abstract

In an earlier paper (Part 1), a parametric state feedback time-optimal control law was devised for the regular Kronecker invariants on the basis of parametrization of the vector companion form. The present paper describes a straight-forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular Kronecker invariants. Hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law. An illustrative example is presented.