Stabilization of linear distributed control systems with unbounded delay

Abstract

In this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay. Assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space, we characterize those systems that can be stabilized using a feedback control. As consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control.  2004 Elsevier Inc. All rights reserved.

Asymptotic stability of nonlinear systems with unbounded delays

“…The stability analysis of time-delay systems receives much attention of researchers [2,6,7,20]. Various analysis techniques such as Lyapunov direct method and characteristic equation method have been utilized to derive criteria for asymptotic stability of the systems [1,11].…”

“…Various analysis techniques such as Lyapunov direct method and characteristic equation method have been utilized to derive criteria for asymptotic stability of the systems [1,11]. Even though there are some stability criteria about systems with unbounded delays [3,4,7,8], most of stability analysis in the literature aim at systems with bounded delays (see [10,13,17] and references therein). As pointed out in [3,12], stability results established for equations with bounded delays are not obviously true in general for unbounded delays.…”