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 the context of continuous-time linear systems, some algebraic positive invariance conditions are established for unbounded symmetrical polyhedra. The existence of a solution to the corresponding set of equations and inequalities depends on the structural properties of an associated input-output system. In particular, the number of zeros of this system should be appropriate and they should be stable. If these conditions are satisfied, the problem can easily be solved by eigenvalue and eigenvector assignment.