Control Canonical Forms and Eigenvalue Assignment by Feedback for a Class of Linear Hyperbolic Systems

Abstract

Canonical forms are developed for a class of linear hyperbolic systems. They are then applied to solve the problem of eigenvalue assignment by distributed feedback and boundary control. The duality of this problem is demonstrated to one of eigenvalue assignment by boundary feedback of an adjoint system subject to distributed control. For both systems it is shown that by feedback, the set $\{ \rho _j \} $, $j \in \mathbb{Z}$, can be assigned as eigenvalues of the closed loop system, subject to an asymptotic condition on the set $\{ \rho _j \} $. The feedback control is explicitly characterized. Analogous results are obtained for the problem of eigenvalue assignment by distributed feedback and distributed control.