正脉冲切换系统的有限时间稳定性分析
Finite-Time Stability of Positive Implusive Switched Systems

作者: 刘越超 , 高彩霞 :内蒙古大学数学科学学院,内蒙古 呼和浩特;

关键词: Lyapunov稳定性有限时间稳定(FTS)正系统正脉冲切换系统Lyapunov Stability Finite-Time Stability Positive Systems Positive Impulsive Switched Systems

摘要:
本文解决了正脉冲切换系统的有限时间稳定性。首先把有限时间稳定的概念推广到正脉冲切换系统,从解的存在性入手,用求解微分方程组的方法,系统的解若满足一些条件,即可证明系统的稳定性。最后给出正脉冲切换系统稳定的充分条件。

Abstract: This paper addresses the finite-time stability of positive impulsive switched systems. First, the concept of finite-time stability is extended to positive impulsive switched systems, starting from the existence of solutions and solving differential equations. If the solution of the systems satisfies some conditions, then we can prove the stability of the system. Finally, the sufficient conditions of positive impulsive switched systems are given.

文章引用: 刘越超 , 高彩霞 (2015) 正脉冲切换系统的有限时间稳定性分析。 理论数学, 5, 89-94. doi: 10.12677/PM.2015.53014

参考文献

[1] Dorato, P. (1961) Short time stability in linear time-varying systems. In: Proceedings of the IRE international Convention Record Part 4, New York, 9 May 1961, 83-87.

[2] Weiss, L. and Infante, E.F. (1967) Finite time stability under perturbing forces and on product spaces. IEEE Transactions on Automatic Control, 12, 54-59.

[3] Shorten, R., Wirth, F. and Leith, D. (2006) A positive systems model of TCP-like congestion control: Asymptotic results. IEEE/ACM Transactions on Networking, 14, 616-629.

[4] Berman, A., Shorten, R. and Leith, D. (2004) Positive matrices asso-ciated with synchronized communication networks. Linear Algebra and Its Applications, 393, 47-54.

[5] Varga, E.H., Middleton, R., Colaneri, P. and Blanchini, F. (2011) Discrete-time control for switched positive systems with application to mitigating viral escape. International Journal of Robust and Nonlinear Control, 21, 1093-1111.

[6] Commault, C. and Marchand, N. (2006) Positive systems. Proceedings of the Second Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 06), Grenoble, 30 August-1 September 2006, 429- 443.

[7] Commault, C. and Marchand, N. (2006) Multidisciplinary international symposium positive systems No. 2. In: Lecture Notes in Control and Information, Vol. 341, Grenoble, France, 49-56.

[8] Mason, O. and Shorten, R. (2007) On linear co-positive Lyapunov functions and the stability of switched positive linear systems. IEEE Transactions on Automatic Control, 52, 1346-1349.

[9] Gurvits, L., Shorten, R. and Mason, O. (2007) On the stability of switched positive linear systems. IEEE Transactions on Automatic Control, l52, 1099-1103.

[10] Knorn, F., Mason, O. and Shorten, R. (2009) On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica, 45, 1943-1947.

[11] Liu, X. (2009) Stability analysis of switched positive systems: A switched linear co-positive Lyapunov function method. IEEE Transactions on Circuits and Systems II: Express Briefs, 56, 414-418.

[12] Fornasini, E. and Valcher, M.E. (2012) Stability and stabilizability criteria for discrete-time positive switched systems. IEEE Transactions on Automatic Control, 57, 1208-1221.

[13] Zhao, X., Zhang, L., Shi, P. and Liu, M. (2012) Stability of switched positive linear systems with average dwell time switching. Automatica, 48, 1132-1137.

[14] Amato, F., Ariola, M., Cosentino, C., Abdallah, C.T. and Dorato, P. (2003) Necessary and sufficient conditions for finite- time stability of linear systems. In: Proceedings of the American Control Conference, Denver, 4-6 June 2003, 4452- 4456.

[15] Amato, F., Ariola, M. and Cosentino, C. (2005) Finite-time control of linear time-varying Systems via output feedback. In: Proceedings of the American Control Conference, Portland, 8-10 June 2005, 4723-4727.

[16] Amato, F., Ambrosino, R., Cosentino, C. and De Tommasi, G. (2011) Finite-time stabilization of impulsive dynamical linear system. Nonlinear Analysis: Hybrid Systems, 5, 89-101.

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