摘要
This article discusses the Lyapunov-Krasovskii functional method for the stability problem of coupled differentialfunctional equations with distributed delays and one discrete delay. By means of an equivalent expression of the system, the solution of the original system is obtained by using the fundamental solution. Furthermore, a complete Lyapunov-Krasovskii is obtained, which is necessary and sufficient for the distributed delay system. The functional may be easily extended to deal with the stability problem of uncertain systems with distributed delay via the discretization.
This article discusses the Lyapunov-Krasovskii functional method for the stability problem of coupled differentialfunctional equations with distributed delays and one discrete delay. By means of an equivalent expression of the system, the solution of the original system is obtained by using the fundamental solution. Furthermore, a complete Lyapunov-Krasovskii is obtained, which is necessary and sufficient for the distributed delay system. The functional may be easily extended to deal with the stability problem of uncertain systems with distributed delay via the discretization.
引文
[1]Gu K,Liu Y,Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations.Automatica2009;45:798–804.
[2]Gu K.Stability problem of systems with multiple delay channels.Automatica 2010;46:743–751.
[3]Li H,Gu K.Discretized Lyapunov Krasovskii functional for coupled differential difference equations with multiple delay channels.Automatica 2010;46:902–909.
[4]Rˇasvan V,Niculescu S-I.Oscillations in lossless propagation models:a Liapunov CKrasovskii approach.IMA Journal of Mathematical Control and Information 2002;19:157C-172.
[5]Hale JK,Verduyn Lunel SM.Introduction to Functional Differential Equations.Springer:New York,1993.
[6]Rˇasvan V.Dynamical systems with lossless propagation and neutral functional differential equations.Proceedings of MTNS98,Padoue,Italy,1998;527C-531.
[7]Niculescu S-I.Delay effects on stability?a robust control approach.Lecture Notes in Control and Information Science.Springer:London,2001.
[8]Li H,Gu K.Discretized Lyapunov-Krasovskii functional method for coupled differential-difference equations with discrete and distributed delay.Proc.of 7th Asia Control Reference,Hang Kang,China,Aug.27-29,2009.
[9]Li H.Discretized LKF approach for coupled differentialdifference equations with multiple discrete and distributed delays.International Journal of Robust and Nonlinear Control2012;22:875–891.
[10]Pepe P.On the asymptotic stability of coupled delay differential and continuous time difference equations.Automatica2005;41:107–112.
[11]Pepe P,Jiang ZP,Fridman E.A new Lyapunov-Krasovskii methodology for coupled delay differential and difference equations.International Journal of Control 2007;81:107–115.
[12]Gu K,Niculescu SI.Stability Analysis of Time-Delay Systems:A Lyapunov Approach.In:Advanced Topics in Control Systems Theory,Lecture Notes from FAP 2005,Springer:London(Eds:A.Lor′?a,F.Lamnabhi-Lagarrigue,&E.Panteley)2006;139–170.
[13]Gu K,Kharitonov VL,Chen J.Stability of Time-Delay Systems.Birkh¨auser:Boston,MA,2003.
[14]Melchor-Aguilar D.Exponential stability of Linear continuous time difference systems with multiple delays.Syatems&Control Letters 2013;62:811–818.
[15]Li H.Refined Stability of a Class of CDFE with Distributed Delays.Proc.of 34th Chinese Control Conference,Hangzhou,China,July 27-29,2015.
[16]Li H.Stability of CDFEs With Multiple Known and Unknown Delays:Discretized LKF Approach.Advance in Engineering Reeasch(ICACIE 2016),2016,64:0139–0144.
