Asymptotic Hyperstability of Dynamic Systems with Point Delays

M De La Sen

doi:10.3844/ajassp.2005.1279.1282

Abstract

It is proved that a linear time-invariant system with internal point delays is asymptotically hyperstable independent of the delays if an associate delay-free system is asymptotically hyperstable and the delayed dynamics are sufficiently small.

Highlights

Global Lyapunovs stability configurations consisting of linear time-invariant systems in the forward loop with arbitrary nonlinear devices satisfying Popovstype time-integral inequalities are the so-called hyperstability property[1,2,3]
The importance of the topic relies on the fact that the stability property holds for all nonlinearity satisfying Popovs in equality for all time. In this brief, related results are obtained when the linear plant is subject to a finite number of bounded incommensurate delays (i.e. The delays are not necessarily an integer multiple of a real number) if its associated dynamics are sufficiently small
The study of stability/hyperstability properties for systems involving external (i.e. In the inputs or outputs) delays may be addressed by direct extensions from the analysis methods concerning delay-free systems by transforming the relevant signals in new ones influenced by delays[2,4,5]

Summary

Introduction

Global Lyapunovs stability (asymptotic stability) configurations consisting of linear time-invariant systems in the forward loop with arbitrary nonlinear (and, perhaps time-varying) devices satisfying Popovstype time-integral inequalities are the so-called hyperstability (asymptotic hyperstability) property[1,2,3]. In this brief, related results are obtained when the linear plant is subject to a finite number of bounded incommensurate delays (i.e. The delays are not necessarily an integer multiple of a real number) if its associated dynamics are sufficiently small. The asymptotic hyperstability of continuous time-delay systems is focused on for systems including any finite number of incommensurate internal point delays of arbitrary sizes provided that the plant free of delayed dynamics satisfies a strict positive realness condition.

Results

Conclusion