Feedback stabilization of infinite-dimensional systems with Aγ-bounded output operators

Abstract

This paper is concerned with the stabilization problem of infinite-dimensional systems with A γ-bounded output operators. An operator is said to be A γ-bounded if it can be written as C( A+ c) γ for some bounded operator C and some scalar c (see [1]). For example, the linear diffusion system with distributed (or boundary) control and boundary observation is formulated as an evolution equation with bounded input operator and A γ-bounded output operator in a Hilbert space. The purpose of this paper is to show that the closed-loop system with a finite-dimensional controller containing residual mode filter, which Balas introduced for infinite-dimensional systems with bounded input and output operators, is exponentially stable if the order of residual mode filter is chosen sufficiently large.