Stabilization of Delay Systems: Delay-Dependent Impulsive Control

doi:10.1109/TAC.2016.2530041

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Stabilization of Delay Systems: Delay-Dependent Impulsive Control

Journal Article•DOI•

Stabilization of Delay Systems: Delay-Dependent Impulsive Control

Xiaodi Li¹, Shiji Song²•Institutions (2)

Shandong Normal University¹, Tsinghua University²

01 Jan 2017-IEEE Transactions on Automatic Control (IEEE)-Vol. 62, Iss: 1, pp 406-411

TL;DR: It is shown that time delays in impulse term may contribute to the stabilization of delay systems, and an impulsive delay inequality is proposed which applies to the delay systems which may be originally unstable, and derive some delay-dependent impulsive control criteria to ensure the stabilize of the addressed systems.

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Abstract: The stabilization problem of delay systems is studied under the delay-dependent impulsive control. The main contributions of this technical note are that, for one thing, it shows that time delays in impulse term may contribute to the stabilization of delay systems, that is, a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks; for another, it shows the robustness of impulsive control, that is, the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization. In this technical note, from impulsive control point of view we firstly propose an impulsive delay inequality. Then we apply it to the delay systems which may be originally unstable, and derive some delay-dependent impulsive control criteria to ensure the stabilization of the addressed systems. The effectiveness of the proposed strategy is evidenced by two illustrative examples.

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Journal Article•DOI•

Finite-time stability and settling-time estimation of nonlinear impulsive systems

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Xiaodi Li¹, Daniel W. C. Ho², Jinde Cao³•Institutions (3)

Shandong Normal University¹, City University of Hong Kong², Southeast University³

01 Jan 2019-Automatica

TL;DR: It is shown that the settling-time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect, and several Lyapunov-based FTS theorems involving stabilizing impulses and destabilizing impulses are established.

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230 citations

Journal Article•DOI•

Persistence of delayed cooperative models: Impulsive control method

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Xiaodi Li¹, Xueyan Yang¹, Tingwen Huang²•Institutions (2)

Shandong Normal University¹, Texas A&M University at Qatar²

01 Feb 2019-Applied Mathematics and Computation

TL;DR: The results show that proper impulsive control strategy may contribute to the persistence of cooperative populations and maintain the balance of an ecosystem.

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214 citations

Journal Article•DOI•

Consensus of Leader-Following Multiagent Systems: A Distributed Event-Triggered Impulsive Control Strategy

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Xuegang Tan¹, Jinde Cao¹, Xiaodi Li²•Institutions (2)

Southeast University¹, Shandong Normal University²

01 Mar 2019-IEEE Transactions on Systems, Man, and Cybernetics

TL;DR: This paper investigates the leader-following consensus problem of multiagent systems using a distributed event-triggered impulsive control method and shows that continuous communication of neighboring agents can be avoided, and Zeno-behavior can be excluded in the schema.

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Abstract: This paper investigates the leader-following consensus problem of multiagent systems using a distributed event-triggered impulsive control method. For each agent, the controller is updated only when some state-dependent errors exceed a tolerable bound. The control inputs will be carried out by actor only at event triggering impulsive instants. According to the Lyapunov stability theory and impulsive method, several sufficient criteria for leader-following consensus are derived. Also, it is shown that continuous communication of neighboring agents can be avoided, and Zeno-behavior can be excluded in our schema. The results are illustrated through several numerical simulation examples.

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205 citations

Cites background from "Stabilization of Delay Systems: Del..."

...Compared with these continuous control methods, impulsive control as a class of discontinuous control methods usually have a relatively simple structure and have been successfully applied in many disciplines [28]–[30]....
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Journal Article•DOI•

Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback

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Dan Yang¹, Xiaodi Li¹, Jianlong Qiu²•Institutions (2)

Shandong Normal University¹, Linyi University²

01 May 2019-Nonlinear Analysis: Hybrid Systems

TL;DR: A state-dependent switching rule and the switching regions are proposed and the stability and tracking performance analysis are proposed based on single Lyapunov function technique, respectively and the design problem of dynamic output feedback controllers can be solved efficiently by using linear matrix inequalities (LMIs) toolbox.

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192 citations

Journal Article•DOI•

Lyapunov Stability for Impulsive Systems via Event-Triggered Impulsive Control

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Xiaodi Li¹, Dongxue Peng¹, Jinde Cao²•Institutions (2)

Shandong Normal University¹, Southeast University²

07 Jan 2020-IEEE Transactions on Automatic Control

TL;DR: This article investigates the Lyapunov stability problem for impulsive systems via event-triggered impulsive control, where dynamical systems evolve according to continuous-time equations most of the time, but occasionally exhibit instantaneous jumps when impulsive events are triggered.

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Abstract: In this article, we investigate the Lyapunov stability problem for impulsive systems via event-triggered impulsive control, where dynamical systems evolve according to continuous-time equations most of the time, but occasionally exhibit instantaneous jumps when impulsive events are triggered. We provide some Lyapunov-based sufficient conditions for uniform stability and globally asymptotical stability. Unlike normal time-triggered impulsive control, event-triggered impulsive control is triggered only when an event occurs. Thus our stability conditions rely greatly on the event-triggering mechanism given in terms of Lyapunov functions. Moreover, the Zeno behavior can be excluded in our results. Then, we apply the theoretical results to the nonlinear impulsive control system, where event-triggered impulsive control strategies are designed to achieve stability of the addressed system. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the proposed results.

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174 citations

Cites background or methods from "Stabilization of Delay Systems: Del..."

...Compared with the traditional time-triggered impulsive schemes, such as those in [5]–[8], [14], and [15], Theorem 1 does not impose any direct restriction on time intervals, and the triggering time is completely determined by the designed ETM....
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...2964558 number of scholars from different fields have focused on the investigation of designing impulsive control strategies for various modelings (see [14]–[16] and the references therein)....
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References

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Book•

Introduction to Functional Differential Equations

[...]

Jack K. Hale, Sjoerd M. Verduyn Lunel

14 Oct 1993

TL;DR: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977 and attempts to maintain the spirit of that book and have retained approximately one-third of the material intact.

...read moreread less

Abstract: The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a completely new presentation of linear systems (Chapter 6-9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive.

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6,844 citations

"Stabilization of Delay Systems: Del..." refers background in this paper

...INTRODUCTION DELAY systems have been extensively studied in last decades due to their widely applications in many fields such as neural networks [1], [2], biology [3], manufacturing processes [4] and information technology [5], [6], and there are significant contributions in the literatures, see [7]-[13]....
[...]

Book•

Stability of Time-Delay Systems

[...]

Kequin Gu, Jie Chen, Vladimir L. Kharitonov

26 Jun 2003

TL;DR: Preface, Notations 1.Introduction to Time-Delay Systems I.Robust Stability Analysis II.Input-output stability A.LMI and Quadratic Integral Inequalities Bibliography Index

...read moreread less

Abstract: Preface, Notations 1.Introduction to Time-Delay Systems I.Frequency-Domain Approach 2.Systems with Commensurate Delays 3.Systems withIncommensurate Delays 4.Robust Stability Analysis II.Time Domain Approach 5.Systems with Single Delay 6.Robust Stability Analysis 7.Systems with Multiple and Distributed Delays III.Input-Output Approach 8.Input-output stability A.Matrix Facts B.LMI and Quadratic Integral Inequalities Bibliography Index

...read moreread less

4,200 citations

Book•

Stability and Oscillations in Delay Differential Equations of Population Dynamics

[...]

K. Gopalsamy

31 Mar 1992

TL;DR: The Delay Logistic Equation (DLE) as mentioned in this paper is a delay-induced Bifurcation to Periodicity (DBE) model for deterministic linear systems.

...read moreread less

Abstract: 1. The Delay Logistic Equation. 2. Delay Induced Bifurcation to Periodicity. 3. Methods of Linear Analysis. 4. Global Attractivity. 5. Models of Neutral Differential Systems. References. Index.

...read moreread less

2,007 citations

"Stabilization of Delay Systems: Del..." refers background in this paper

...dynamics such as fishing industry [16], effective impulsive control such as harvesting and releasing can keep the balance of fishing, and the quantities of every impulsive harvesting or releasing are not only measured by the current numbers of fish but also depend on the numbers in recent history due to the fact that the immature fish need some time to grow....
[...]

Journal Article•DOI•

Wirtinger-based integral inequality: Application to time-delay systems

[...]

Alexandre Seuret¹, Frédéric Gouaisbaut¹•Institutions (1)

Hoffmann-La Roche¹

01 Sep 2013-Automatica

TL;DR: An alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities is proposed and it is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions.

...read moreread less

1,791 citations

Journal Article•DOI•

Stability of time-delay systems

[...]

J. G. Landis¹, Daniel D. Perlmutter¹•Institutions (1)

University of Pennsylvania¹

01 Mar 1972-Aiche Journal

TL;DR: In this article, a direct method for determining both local and regional stability of systems described by nonlinear differential-difference equations is presented, with respect to a general class of initial curves.

...read moreread less

Abstract: A direct method is presented for determining both local and regional stability of systems described by nonlinear differential-difference equations. Prediction of stability is with respect to a general class of initial curves. The practical as well as the conservative nature of the procedure is demonstrated by a numerical example.

...read moreread less

1,087 citations

"Stabilization of Delay Systems: Del..." refers background or result in this paper

...When there is no impulsive effect, some results for stability of system (17) have been derived, see ([6], [10], [26], [27]....
[...]
...In addition, compared with the existing results without impulses, such as those in [6], [10], [26], [27] in which the upper and lower bound of time delays are imposed to ensure the stability, we show that the stability of those system can be derived for any time delays via the delay-dependent impulsive control....
[...]
...As a class of infinite dimensional systems, delay systems usually have complicated structures which lead to complex dynamics [6], [13]....
[...]
...INTRODUCTION DELAY systems have been extensively studied in last decades due to their widely applications in many fields such as neural networks [1], [2], biology [3], manufacturing processes [4] and information technology [5], [6], and there are significant contributions in the literatures, see [7]-[13]....
[...]