Robustness Analysis of Global Exponential Stability of Nonlinear Systems with Generalized Piecewise Constant Arguments
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- 英文论文题名：Robustness Analysis of Global Exponential Stability of Nonlinear Systems with Generalized Piecewise Constant Arguments
- 论文作者：Liguang Wan ; Ailong Wu
- 英文论文作者：Liguang Wan ; Ailong Wu ; College of Mechatronics and Control Engineering ; Hubei Normal University ; College of Mathematics and Statistics ; Hubei Normal University
- 年：2017
- 作者机构：College of Mechatronics and Control Engineering,Hubei Normal University;College of Mathematics and Statistics,Hubei Normal University;
- 英文论文关键词：Nonlinear systems ; Global exponential stability ; Robustness ; Generalized piecewise constant arguments
- 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：6
- 文件大小：335k
- 原文格式：D
- 会议级别：全国
摘要
On account of the finite propagation speed of signals, time-delay phenomena are abundant. Compared with timedelay systems, nonlinear systems with generalized piecewise constant arguments can be both of advance and retard, which are an extension to time-delay systems. In this paper, we address the robustness of global exponential stability for a general class of nonlinear systems with generalized piecewise constant arguments, that is, given globally exponentially stable nonlinear systems,the problem that how much intensity of generalized piecewise constant arguments the nonlinear systems can be sustained to maintain globally exponentially stable is investigated. First, conditions guaranteeing the existence and uniqueness of solution for a general class of nonlinear systems with generalized piecewise constant arguments are formulated. Furthermore, the upper bound of the intensity of generalized piecewise constant arguments can be obtained to keep the nonlinear systems to be globally exponentially stable by solving the transcendental equation. Finally, one numerical example is presented to show the effectiveness of theoretical result.
On account of the finite propagation speed of signals, time-delay phenomena are abundant. Compared with timedelay systems, nonlinear systems with generalized piecewise constant arguments can be both of advance and retard, which are an extension to time-delay systems. In this paper, we address the robustness of global exponential stability for a general class of nonlinear systems with generalized piecewise constant arguments, that is, given globally exponentially stable nonlinear systems,the problem that how much intensity of generalized piecewise constant arguments the nonlinear systems can be sustained to maintain globally exponentially stable is investigated. First, conditions guaranteeing the existence and uniqueness of solution for a general class of nonlinear systems with generalized piecewise constant arguments are formulated. Furthermore, the upper bound of the intensity of generalized piecewise constant arguments can be obtained to keep the nonlinear systems to be globally exponentially stable by solving the transcendental equation. Finally, one numerical example is presented to show the effectiveness of theoretical result.
On account of the finite propagation speed of signals, time-delay phenomena are abundant. Compared with timedelay systems, nonlinear systems with generalized piecewise constant arguments can be both of advance and retard, which are an extension to time-delay systems. In this paper, we address the robustness of global exponential stability for a general class of nonlinear systems with generalized piecewise constant arguments, that is, given globally exponentially stable nonlinear systems,the problem that how much intensity of generalized piecewise constant arguments the nonlinear systems can be sustained to maintain globally exponentially stable is investigated. First, conditions guaranteeing the existence and uniqueness of solution for a general class of nonlinear systems with generalized piecewise constant arguments are formulated. Furthermore, the upper bound of the intensity of generalized piecewise constant arguments can be obtained to keep the nonlinear systems to be globally exponentially stable by solving the transcendental equation. Finally, one numerical example is presented to show the effectiveness of theoretical result.
引文
[1]W.Chen and W.X.Zheng,Delay-dependent robust stabilization for uncertain neutral systems with distributed delays,Automatica,2007:95-104.
[2]Q.Han,A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems,Automatica,2008:272-277.
[3]X.Nian,X.Wang,Y.Wang,and Z.Sun,Delay-dependent stability for fuzzy neutral system via state matrix decomposition,IET Control Theory&Applications,2012:1745-1751.
[4]L.Wang,W.Lu,and T.Chen,Multistability and new attraction basins of almost-periodic solutions of delayed neural networks,IEEE Transactions on Neural Networks,2009:1581-1593.
[5]A.Wu and Z.Zeng,Exponential stabilization of memristive neural networks with time delays,IEEE Transactions on Neural Networks and Learning Systems,2012:1919-1929.
[6]H.Huang,G.Feng,and J.Cao,Robust state estimation for uncertain neural networks with time-varying delays,IEEE Transactions on Neural Networks,2008:1329-1339.
[7]T.Huang,C.Li,S.Duan,and J.Starzyk,Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects,IEEE Transactions on Neural Networks and Learning Systems,2012:866-875.
[8]Y.Shen and J.Wang,Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances,IEEE Transactions on Neural Networks and Learning Systems,2012:87-96.
[9]Z.Wang,B.Shen,H.Shu,and G.Wei,Quantized H∞control for nonlinear stochastic time-delay systems with missing measurements,IEEE Transactions on Automatic Control,2012:1431-1444.
[10]H.Li,H.Jiang,and C.Hu,Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays,Neural Networks,2016:97-109.
[11]H.Huang,T.Huang,and X.Chen,Global exponential estimates of delayed stochastic neural networks with Markovian switching,Neural Networks,2010:136-145.
[12]Q.Song,H.Yan,Z.Zhao,and Y.Liu,Global exponential stability of complex-valued neural networks with both timevarying delays and impulsive effects,Neural Networks,2016:108-116.
[13]Y.Shen and J.Wang,Robustness analysis of global exponential stability of non-linear systems with time delays and neutral terms,IET Control Theory&Applications,2013:1227-1232.
[14]W.Chen and W.X.Zheng,Robust stability analysis for stochastic neural networks with time-varying delay,IEEE Transactions on Neural Networks,2010:508-514.
[15]Y.He,J.Zeng,M.Wu,and C.Zhang,Robust stabilization and H∞controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,Mathematical Biosciences,2012:53-63.
[16]A.Wu,L.Liu,T.Huang,and Z.Zeng,Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments,Neural Networks,2017:118-127.
[17]L.Wan and A.Wu,Stabilization control of generalized type neural networks with piecewise constant argument,Journal of Nonlinear Science and Applications,2016:3580-3599.
[18]M.Akhmet,D.Aru?gaslan,and E.Y?lmaz,Stability analysis of recurrent neural networks with piecewise constant argument of generalized type,Neural Networks,2010:805-811.
[19]A.Wu and Z.Zeng,Output convergence of fuzzy neurodynamic systems with piecewise constant argumment of generalized type and timevarying input,IEEE Transactions on Systems,Man,and Cybernetics:Systems,2016:1689-1702.
[2]Q.Han,A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems,Automatica,2008:272-277.
[3]X.Nian,X.Wang,Y.Wang,and Z.Sun,Delay-dependent stability for fuzzy neutral system via state matrix decomposition,IET Control Theory&Applications,2012:1745-1751.
[4]L.Wang,W.Lu,and T.Chen,Multistability and new attraction basins of almost-periodic solutions of delayed neural networks,IEEE Transactions on Neural Networks,2009:1581-1593.
[5]A.Wu and Z.Zeng,Exponential stabilization of memristive neural networks with time delays,IEEE Transactions on Neural Networks and Learning Systems,2012:1919-1929.
[6]H.Huang,G.Feng,and J.Cao,Robust state estimation for uncertain neural networks with time-varying delays,IEEE Transactions on Neural Networks,2008:1329-1339.
[7]T.Huang,C.Li,S.Duan,and J.Starzyk,Robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects,IEEE Transactions on Neural Networks and Learning Systems,2012:866-875.
[8]Y.Shen and J.Wang,Robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances,IEEE Transactions on Neural Networks and Learning Systems,2012:87-96.
[9]Z.Wang,B.Shen,H.Shu,and G.Wei,Quantized H∞control for nonlinear stochastic time-delay systems with missing measurements,IEEE Transactions on Automatic Control,2012:1431-1444.
[10]H.Li,H.Jiang,and C.Hu,Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays,Neural Networks,2016:97-109.
[11]H.Huang,T.Huang,and X.Chen,Global exponential estimates of delayed stochastic neural networks with Markovian switching,Neural Networks,2010:136-145.
[12]Q.Song,H.Yan,Z.Zhao,and Y.Liu,Global exponential stability of complex-valued neural networks with both timevarying delays and impulsive effects,Neural Networks,2016:108-116.
[13]Y.Shen and J.Wang,Robustness analysis of global exponential stability of non-linear systems with time delays and neutral terms,IET Control Theory&Applications,2013:1227-1232.
[14]W.Chen and W.X.Zheng,Robust stability analysis for stochastic neural networks with time-varying delay,IEEE Transactions on Neural Networks,2010:508-514.
[15]Y.He,J.Zeng,M.Wu,and C.Zhang,Robust stabilization and H∞controllers design for stochastic genetic regulatory networks with time-varying delays and structured uncertainties,Mathematical Biosciences,2012:53-63.
[16]A.Wu,L.Liu,T.Huang,and Z.Zeng,Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments,Neural Networks,2017:118-127.
[17]L.Wan and A.Wu,Stabilization control of generalized type neural networks with piecewise constant argument,Journal of Nonlinear Science and Applications,2016:3580-3599.
[18]M.Akhmet,D.Aru?gaslan,and E.Y?lmaz,Stability analysis of recurrent neural networks with piecewise constant argument of generalized type,Neural Networks,2010:805-811.
[19]A.Wu and Z.Zeng,Output convergence of fuzzy neurodynamic systems with piecewise constant argumment of generalized type and timevarying input,IEEE Transactions on Systems,Man,and Cybernetics:Systems,2016:1689-1702.