Exponential Stability for Nonlinear Systems with Time Delay on Time Scales via Wirtinger-Based Inequality
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- 英文论文题名：Exponential Stability for Nonlinear Systems with Time Delay on Time Scales via Wirtinger-Based Inequality
- 论文作者：Xiaodong Lu ; Xianfu Zhang ; Qingrong Liu
- 英文论文作者：Xiaodong Lu ; Xianfu Zhang ; Qingrong Liu ; School of Control Science and Engineering ; Shandong University ; School of Mathematics and Quantitative Economics ; Shandong University of Finance and Economics
- 年：2017
- 作者机构：School of Control Science and Engineering,Shandong University;School of Mathematics and Quantitative Economics,Shandong University of Finance and Economics;
- 英文论文关键词：Exponential stability ; Wirtinger-based inequality ; Time delay ; Time scale
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O175
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：201k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the problem of exponential stability for nonlinear systems with time delay on time scales is investigated.Based on the Wirtinger-based inequality on time scales, and the Lyapunov-Krasovskii functional approach, a sufficient criterion for exponential stability for nonlinear time-delay systems on time scales is derived. It is shown that the idea of this paper provides a unified approach to study the exponential stability problems for continuous-time systems and their discrete-time counterparts simultaneously. To illustrate the effectiveness of our result, two simulation examples are given.
In this paper, the problem of exponential stability for nonlinear systems with time delay on time scales is investigated.Based on the Wirtinger-based inequality on time scales, and the Lyapunov-Krasovskii functional approach, a sufficient criterion for exponential stability for nonlinear time-delay systems on time scales is derived. It is shown that the idea of this paper provides a unified approach to study the exponential stability problems for continuous-time systems and their discrete-time counterparts simultaneously. To illustrate the effectiveness of our result, two simulation examples are given.
In this paper, the problem of exponential stability for nonlinear systems with time delay on time scales is investigated.Based on the Wirtinger-based inequality on time scales, and the Lyapunov-Krasovskii functional approach, a sufficient criterion for exponential stability for nonlinear time-delay systems on time scales is derived. It is shown that the idea of this paper provides a unified approach to study the exponential stability problems for continuous-time systems and their discrete-time counterparts simultaneously. To illustrate the effectiveness of our result, two simulation examples are given.
引文
[1]Zhu X L,Yang G H.Jensen inequality approach to stability analysis of discrete-time systems with time-varying delay,American Control Conference,2008:1644-1649,2008.
[2]Nam P T,Pathirana P N,Trinh H.Discrete Wirtinger-based inequality and its application,Journal of the Franklin Institute,352(5):1893-1905,2015.
[3]Seuret A,Gouaisbaut F.Wirtinger-based integral inequality:application to time-delay systems,Automatica,49(9):2860-2866,2013.
[4]Huang X Y;Oscillatory behavior of n-th-order neutral dynamic equations with mixed nonlinearities on time scales,Electron.J.Diff.Equ.,16(2016),1–18.
[5]Wu H,Erbe L,Peterson A;Oscillation of solution to secondorder half-linear delay dynamic equations on time scales,Electron.J.Diff.Equ.,71(2016),1–15.
[6]Wu H,Jia B,Erbe L;Theorems of Kiguradze-type and Belohorec-type revisited on time scales,Electron.J.Diff.Equ.,71(2015),1–12.
[7]Dogan A;Triple positive solutions for m-point boundaryvalue problems of dynamic equations on time scales with pLaplacian,Electron.J.Differ.Equ.,131(2015),1–12.
[8]Wang N,Zhou H,Yang L;Existence of solutions for fourpoint resonance boundary-value problems on time scales,Electron.J.Diff.Equ.,240(2015),1–10.
[9]Jackson B.Partial dynamic equations on time scales,Journal of Computational and Applied Mathematics,186(2):391-415,2006.
[10]Ptzsche C,Siegmund S,Wirth F.A spectral characterization of exponential stability for linear time-invariant systems on time scales,Discrete Continuous Dynamic Systems,9:1223-1241,2003.
[11]Da Cunha J J.Stability for time varying linear dynamic systems on time scales,Journal of Computational and Applied Mathematics,176(2):381-410,2005.
[12]Da Cunha J J.Instability results for slowly time varying linear dynamic systems on time scales,Journal of Mathematical Analysis and Applications,328(2):1278-1289,2007.
[13]Hoffacker J,Tisdell C C.Stability and instability for dynamic equations on time scales,Computers and Mathematics with Applications,49:1327-1334,2005.
[14]Du N H.On the exponential stability of dynamic equations on time scales,Journal of Mathematical Analysis and Applications,331(2):1159-1174,2007.
[15]Bohner M,Peterson A.Dynamic equations on time scales-an introduction with applications.Birkhauser,Boston,2001.
[16]Lu X,Wang Y,Zhao Y.Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality,Neurocomputing,216:143-149,2016.
[17]Ali M S,Balasubramaniam P,Exponential stability of timedelay systems with nonlinear uncertainties,International Journal of Computer Mathematics,87(6):1363-1373,2010.
[2]Nam P T,Pathirana P N,Trinh H.Discrete Wirtinger-based inequality and its application,Journal of the Franklin Institute,352(5):1893-1905,2015.
[3]Seuret A,Gouaisbaut F.Wirtinger-based integral inequality:application to time-delay systems,Automatica,49(9):2860-2866,2013.
[4]Huang X Y;Oscillatory behavior of n-th-order neutral dynamic equations with mixed nonlinearities on time scales,Electron.J.Diff.Equ.,16(2016),1–18.
[5]Wu H,Erbe L,Peterson A;Oscillation of solution to secondorder half-linear delay dynamic equations on time scales,Electron.J.Diff.Equ.,71(2016),1–15.
[6]Wu H,Jia B,Erbe L;Theorems of Kiguradze-type and Belohorec-type revisited on time scales,Electron.J.Diff.Equ.,71(2015),1–12.
[7]Dogan A;Triple positive solutions for m-point boundaryvalue problems of dynamic equations on time scales with pLaplacian,Electron.J.Differ.Equ.,131(2015),1–12.
[8]Wang N,Zhou H,Yang L;Existence of solutions for fourpoint resonance boundary-value problems on time scales,Electron.J.Diff.Equ.,240(2015),1–10.
[9]Jackson B.Partial dynamic equations on time scales,Journal of Computational and Applied Mathematics,186(2):391-415,2006.
[10]Ptzsche C,Siegmund S,Wirth F.A spectral characterization of exponential stability for linear time-invariant systems on time scales,Discrete Continuous Dynamic Systems,9:1223-1241,2003.
[11]Da Cunha J J.Stability for time varying linear dynamic systems on time scales,Journal of Computational and Applied Mathematics,176(2):381-410,2005.
[12]Da Cunha J J.Instability results for slowly time varying linear dynamic systems on time scales,Journal of Mathematical Analysis and Applications,328(2):1278-1289,2007.
[13]Hoffacker J,Tisdell C C.Stability and instability for dynamic equations on time scales,Computers and Mathematics with Applications,49:1327-1334,2005.
[14]Du N H.On the exponential stability of dynamic equations on time scales,Journal of Mathematical Analysis and Applications,331(2):1159-1174,2007.
[15]Bohner M,Peterson A.Dynamic equations on time scales-an introduction with applications.Birkhauser,Boston,2001.
[16]Lu X,Wang Y,Zhao Y.Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality,Neurocomputing,216:143-149,2016.
[17]Ali M S,Balasubramaniam P,Exponential stability of timedelay systems with nonlinear uncertainties,International Journal of Computer Mathematics,87(6):1363-1373,2010.