Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach

Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert function. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and the response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results.

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Stability and stabilization for a class of fractional-order linear time-delay systems

2017 36th Chinese Control Conference (CCC) ◽

10.23919/chicc.2017.8029167 ◽

2017 ◽

Cited By ~ 1

Author(s):

Zhao Yige ◽

Xu Meirong

Keyword(s):

Time Delay ◽

Fractional Order ◽

Linear Time ◽

Delay Systems ◽

Time Delay Systems ◽

Order Linear ◽

Stability And Stabilization

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Introduction

Delay-Adaptive Linear Control ◽

10.23943/princeton/9780691202549.003.0001 ◽

2020 ◽

pp. 1-16

Author(s):

Yang Zhu ◽

Miroslav Krstic

Keyword(s):

Time Delay ◽

Linear Time ◽

Delay Systems ◽

Engineering Practice ◽

Time Delay Systems ◽

Feedback Systems ◽

Deviating Argument ◽

Linear Time Invariant ◽

Feedback Laws ◽

Input Delays

This introductory chapter provides an overview of time-delay systems. Time-delay systems, also called systems with after-effect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations, are ubiquitous in practice. Some representative examples are found in chemical industry, electrical and mechanical engineering, biomedical engineering, and management and traffic science. The most common forms of time delay in dynamic phenomena that arise in engineering practice are actuator and sensor delays. Due to the time it takes to receive the information needed for decision-making, to compute control decisions, and to execute these decisions, feedback systems often operate in the presence of delays. The chapter then illustrates the possible methods in control of time-delay systems. This book develops adaptive and robust predictor feedback laws for the compensation of the five uncertainties for general linear time-invariant (LTI) systems with input delays.

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State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach

Numerical Linear Algebra with Applications ◽

10.1002/nla.731 ◽

2011 ◽

Vol 18 (3) ◽

pp. 351-361 ◽

Cited By ~ 16

Author(s):

Rajeeb Dey ◽

Sandip Ghosh ◽

G. Ray ◽

A. Rakshit

Keyword(s):

Time Delay ◽

State Feedback ◽

Linear Time ◽

Feedback Stabilization ◽

Delay Systems ◽

Matrix Inequality ◽

Time Delay Systems ◽

Nonlinear Matrix Inequality ◽

Nonlinear Matrix

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Parameterization approach to stability and feedback stabilization of linear time-delay systems

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1243/09596518jsce802 ◽

2009 ◽

Vol 223 (7) ◽

pp. 929-939

Author(s):

M S Mahmoud ◽

A Ismail ◽

F M Al-Sunni

Keyword(s):

Time Delay ◽

Linear Time ◽

Delay System ◽

Feedback Stabilization ◽

Delay Systems ◽

Linear Matrix ◽

Parameter Uncertainties ◽

Systematic Analysis ◽

Feedback Scheme ◽

Delay Dependent

This paper develops a new parameterized approach to the problems of delay-dependent analysis and feedback stabilization for a class of linear continuous-time systems with time-varying delays. An appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics. The construction guarantees avoiding bounding methods and effectively deploying injecting parametrized variables to facilitate systematic analysis. Delay-dependent stability provides a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear time-delay system is asymptotically stable with a γ-level £2 gain. By delay-dependent stabilization, a state-feedback scheme is designed to guarantee that the closed-loop switched system enjoys the delay-dependent asymptotic stability with a prescribed γ-level £2 gain. It is established that the methodology provides the least conservatism in comparison with other published methods. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.

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