(A, B)-Invariance conditions of polyhedral domains for continuous-time systems

Abstract

This paper provides an explicit characterisation of the (A,B)-invariance property of polyhedral sets with respect to linear continuous-time systems. A typical application of the concept of (A,B)-invariance is to investigate the possibility of controlling a system subject to pointwise in time trajectory constraints. Necessary and sufficient conditions for a polyhedron to be (A,B)-invariant are established in the form of linear matrix relations. Some particular conditions of existence of linear state feedback laws are also presented. The study of (A,B)-invariance of polyhedra is then extended to the control of constrained and additively disturbed systems.