Eigenstructure assignment for state constrained linear continuous time systems

Linear state constraints define a polyhedron in the state space of a dynamical system. If this polyhedron can be made positively invariant by state feedback, the constraints are satisfied all along the trajectory for any initial point in this polyhedron. In this paper, some algebraic invariance relations are established for continuous-time linear systems. The existence of a solution to the corresponding set of equations and inequalities depends of the structural properties of an associated input-output system. In particular, the number of invariant zeros of this system should be appropriate. If these conditions are satisfied, the problem can easily be solved by eigenvalue and eigenvector assignment.