Stability Analysis of Time Delayed System with Coefficient Uncertainty and Time Delay Uncertainty

doi:10.3166/ejc.16.5-13

European Journal of Control

Volume 16, Issue 1, 2010, Pages 5-13

https://doi.org/10.3166/ejc.16.5-13 Get rights and content

A general class of linear time invariant (LTI) systems with uncertain coefficient and time delay is studied. This study proposes an approach to determine the joint stability regions of uncertain parameters in both time delay space and coefficient space. The stability boundaries in coefficient-delay space are first obtained by determining stability boundaries in coefficient space. To achieve this, a bilinear transformation is used to transform quasipolynomial into polynomial and the subtle feature of Routh array is exploited. After generating stability boundaries in parametric space, a two-step determination procedure is proposed to extend the paradigm called “cluster treatment of characteristic roots (CTCR)” to the determination of stability regions in coefficient-delay space. A complete example case study is also provided.

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Stability Analysis of Time Delayed System with Coefficient Uncertainty and Time Delay Uncertainty

Stable polyhedra in parameter space

Automatica

Differential– Difference Equations

Stabilization of discrete-time systems by first-order controllers

IEEE Trans Autom Control

Delay independent stability conditions and decay estimates for time-varying functional differential equations

IEEE Trans Autom Control

A generalization of Kharitonov's theorem: robust stability of interval plants

IEEE Trans Autom Control

Frequency sweeping tests for stability independent of delay

IEEE Trans Autom Control

Introduction to the Theory and Application of Differential Equations with Deviating Arguments

Stability robustness analysis of multiple time-delayed systems using “building block” concept

IEEE Trans Autom Control

Robust stability for time-delayed systems: The edge theorem and graphical tests

IEEE Trans Autom Control

Global geometry of the stable regions for two delay differential equations

J Math Anal Appl

Stabilization of first-order plus dead-time unstable processes using PID controllers

IEE Proc., Control Theory Appl

Linear systems with commensurate time delays: Stability and stabilization independent of delay

IEEE Trans Autom Control

Robust stability analysis of time delay systems: A survey

Annu Rev Control

Robust stability of time-delay systems

IEEE Trans Autom Control