BOUNDED FEEDBACK STABILIZATION AND GLOBAL SEPARATION PRINCIPLE OF DISTRIBUTED-PARAMETER SYSTEMS

In this paper, we show that the infinite-dimensional system Sigma: x(t ) = Ax(t) + Bu(t), x(0) is an element of H is globally strongly asympt otically stabilizable by an arbitrarily small smooth feedback, Here, t he operator A is the infinitesimal generator of a C-0 semigroup of con tractions e(tA) on real Hilbert space H and B is a bounded linear oper ator mapping a Hilbert space of controls ii into H, An explicit smooth feedback control law is given. Further, we identify the class of pert urbations for which the system is still stabilizable by the same feedb ack law as for the nominal system, Based on these results and some dif ferential Lyapunov operator equations, we then establish a global sepa ration principle for the system Sigma with a Kalman-like observer. Fin ally, these results are illustrated via an example dealing with the wa ve equation.