电邮这篇文章 CONSTRUCTING DIAGONAL LYAPUNOV–KRASOVSKII FUNCTIONALS FOR A CLASS OF POSITIVE DIFFERENTIAL-ALGEBRAIC SYSTEMS
- 作者: Aleksandrov A.Y.1
-
隶属关系:
- Saint Petersburg State University
- 期: 卷 60, 编号 5 (2024)
- 页面: 579-589
- 栏目: ORDINARY DIFFERENTIAL EQUATIONS
- URL: https://ogarev-online.ru/0374-0641/article/view/259930
- DOI: https://doi.org/10.31857/S0374064124050013
- EDN: https://elibrary.ru/LBUEJV
- ID: 259930
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
A coupled system describing the interaction of a differential subsystem with nonlinearities of a sector type and a linear difference subsystem is considered. It is assumed that the system is positive. A diagonal Lyapunov–Krasovskii functional is constructed and conditions are determined under which the absolute stability of the investigated system can be proved with the aid of such a functional. In the case of nolinearities of the power form, estimates for the convergence rate of solution to the origin are derived. The stability analysis of the corresponding system with parameter switching is fulfiled. Sufficient conditions guaranteeing the asymptotic stability of the zero solution for any admissible switching law are obtained.
参考
- Niculescu, S.-I. Delay Effects on Stability. A Robust Control Approach / S.-I. Niculescu. — Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milano ; Paris ; Singapur ; Tokyo : Springer, 2001. — 388 p.
- Fridman, E. Introduction to Time-Delay Systems: Analysis and Control / E. Fridman. — Basel : Birkh¨auser, 2014. — 362 p.
- Pepe, P. A new Lyapunov–Krasovskii methodology for coupled delay differential and difference equations / P. Pepe, Z.-P. Jiang, E. Fridman // Int. J. Control. — 2007. — V. 81, № 1. — P. 107–115.
- Rasvan, V. Oscillations in lossless propagation models: a Liapunov–Krasovskii approach / V. Rasvan, S.-I. Niculescu // IMA J. Math. Control Inform. — 2002. — V. 19. — P. 157–172.
- Gu, K. Lyapunov–Krasovskii functional for uniform stability of coupled differential-functional equations / K. Gu, Y. Liu // Automatica. — 2009. — V. 45. — P. 798–804.
- Метельский, А.В. Синтез регуляторов успокоения решения вполне регулярных дифференциально-алгебраических систем с запаздыванием / А.В. Метельский, В.Е. Хартовский // Дифференц. уравнения. — 2017. — Т. 53, № 4. — С. 547–558.
- Щеглова, А.А. Робастная устойчивость дифференциально-алгебраических уравнений произвольного индекса неразрешенности / А.А. Щеглова, А.Д. Кононов // Автоматика и телемеханика. — 2017. — № 5. — С. 36–55.
- Щеглова, А.А. К вопросу о сверхустойчивости интервального семейства дифференциальноалгебраических уравнений / А.А. Щеглова // Автоматика и телемеханика. — 2021. — № 2. — С. 55–70.
- Pepe, P. On the stability of coupled delay differential and continuous time difference equations / P. Pepe, E.I. Verriest // IEEE Trans. on Automatic Control. — 2003. — V. 48, № 8. — P. 1422–1427.
- Ngoc, P.H.A. Stability of coupled functional differential-difference equations / P.H.A. Ngoc // Int. J. Control. — 2020. — V. 93, № 8. — P. 1920–1930.
- Shen, J. Positivity and stability of coupled differential-difference equations with time-varying delays / J. Shen, W.X. Zheng // Automatica. — 2015. — V. 57. — P. 123–127.
- Briat, C. Stability and performance analysis of linear positive systems with delays using input–output methods / C. Briat // Int. J. Control. — 2017. — V. 91, № 7. — P. 1669–1692.
- Aleksandrov, A.Y. Absolute stability and Lyapunov–Krasovskii functionals for switched nonlinear systems with time-delay / A.Y. Aleksandrov, O. Mason // J. Franklin Institute. — 2014. — V. 351, № 8. — P. 4381–4394.
- Kazkurewicz, E. Matrix Diagonal Stability in Systems and Computation / E. Kazkurewicz, A. Bhaya. — Boston : Birkh¨auser, 1999. — 267 p.
- Mason, O. Diagonal Riccati stability and positive time-delay systems / O. Mason // Systems and Control Letters. — 2012. — V. 61. — P. 6–10.
- Aleksandrov A. Diagonal Riccati stability and applications / A. Aleksandrov, O. Mason // Linear Algebra and its Appl. — 2016. — V. 492. — P. 38–51.
- Александров, А.Ю. О диагональной устойчивости позитивных систем с переключениями и запаздыванием / А.Ю. Александров, О. Мейсон // Автоматика и телемеханика. — 2018. — № 12. — С. 16–33.
- Liberzon, D. Basic problems in stability and design of switched systems / D. Liberzon, A.S. Morse // IEEE Control Systems Magazine. — 1999. — V. 19, № 5. — P. 59–70.
- Pastravanu, O.C. Max-type copositive Lyapunov functions for switching positive linear systems / O.C. Pastravanu, M.-H. Matcovschi // Automatica. — 2014. — V. 50. — P. 3323–3327.
- Aleksandrov, A.Y. On the existence of a common Lyapunov function for a family of nonlinear positive systems / A.Y. Aleksandrov // Systems and Control Letters. — 2021. — V. 147. — Art. 1048324.
- Aleksandrov, A.Y. On the existence of diagonal Lyapunov–Krasovskii functionals for a class of nonlinear positive time-delay systems / A.Y. Aleksandrov // Automatica. — 2024. — V. 160. — Art. 111449.
补充文件
