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Erschienen in:

23.08.2024

Practical Exponential Stability of Positive Switched Linear System and Its Application in Practical Consensus of Multi-agent System

verfasst von: Yanhao Ju, Fanwei Meng, Yuangong Sun

Erschienen in: Circuits, Systems, and Signal Processing | Ausgabe 12/2024

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Abstract

In this technical note, we investigate the practical exponential stability of a positive switched linear system with impulses and all subsystems unstable. By constructing two types of switched discretized Lyapunov functions, we give some new sufficient conditions such that the system achieves practical exponential stability under mode-dependent range dwell time switching. Following this, we apply these results to the practical consensus of multi-agent system under switching topologies. The mathematical analysis is validated by a set of numerical examples.

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Literatur
1.
Zurück zum Zitat C. Briat, Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems. Nonlinear Anal. Hybrid Syst. 24, 198–226 (2017)MathSciNetCrossRef C. Briat, Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems. Nonlinear Anal. Hybrid Syst. 24, 198–226 (2017)MathSciNetCrossRef
2.
Zurück zum Zitat S. Bundfuss, M. Dür, Copositive lyapunov functions for switched systems over cones. Syst. Control Lett. 58(5), 342–345 (2009)MathSciNetCrossRef S. Bundfuss, M. Dür, Copositive lyapunov functions for switched systems over cones. Syst. Control Lett. 58(5), 342–345 (2009)MathSciNetCrossRef
3.
Zurück zum Zitat L. Carrillo, W. Russell, J. Hespanha, G. Collins, State estimation of multiagent systems under impulsive noise and disturbances. IEEE Trans. Control Syst. Technol. 23(1), 13–26 (2014)CrossRef L. Carrillo, W. Russell, J. Hespanha, G. Collins, State estimation of multiagent systems under impulsive noise and disturbances. IEEE Trans. Control Syst. Technol. 23(1), 13–26 (2014)CrossRef
4.
Zurück zum Zitat E. Fornasini, M.E. Valcher, Linear copositive Lyapunov functions for continuous-time positive switched systems. IEEE Trans. Automat. Control 55(8), 1933–1937 (2010)MathSciNetCrossRef E. Fornasini, M.E. Valcher, Linear copositive Lyapunov functions for continuous-time positive switched systems. IEEE Trans. Automat. Control 55(8), 1933–1937 (2010)MathSciNetCrossRef
5.
Zurück zum Zitat E. Fornasini, M.E. Valcher, Stability and stabilizability criteria for discrete-time positive switched systems. IEEE Trans. Automat. Control 57(5), 1208–1221 (2011)MathSciNetCrossRef E. Fornasini, M.E. Valcher, Stability and stabilizability criteria for discrete-time positive switched systems. IEEE Trans. Automat. Control 57(5), 1208–1221 (2011)MathSciNetCrossRef
6.
Zurück zum Zitat A. Jadbabaie, J. Lin, A.S. Morse, Co-ordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48(6), 988–1001 (2003)MathSciNetCrossRef A. Jadbabaie, J. Lin, A.S. Morse, Co-ordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Control 48(6), 988–1001 (2003)MathSciNetCrossRef
7.
Zurück zum Zitat Y. Ju, F. Meng, Y. Sun, New criteria for exponential stability of positive switched linear impulsive systems with all modes unstable and its application. Math. Method. Appl. Sci. 52, 1–13 (2021) Y. Ju, F. Meng, Y. Sun, New criteria for exponential stability of positive switched linear impulsive systems with all modes unstable and its application. Math. Method. Appl. Sci. 52, 1–13 (2021)
8.
Zurück zum Zitat Y. Ju, Y. Sun, Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function. Automatica 114, 108836 (2020)MathSciNetCrossRef Y. Ju, Y. Sun, Stabilization of discrete-time switched positive linear systems via weak switched linear copositive Lyapunov function. Automatica 114, 108836 (2020)MathSciNetCrossRef
9.
Zurück zum Zitat Y. Li, H. Zhang, Dwell time stability and stabilization of interval discrete-time switched positive linear systems. Nonlinear Anal. Hybrid Syst. 33, 116–129 (2019)MathSciNetCrossRef Y. Li, H. Zhang, Dwell time stability and stabilization of interval discrete-time switched positive linear systems. Nonlinear Anal. Hybrid Syst. 33, 116–129 (2019)MathSciNetCrossRef
10.
Zurück zum Zitat X. Liu, C. Dang, Stability analysis of positive switched linear systems with delays. IEEE Trans. Automat. Control 56(7), 1684–1690 (2011)MathSciNetCrossRef X. Liu, C. Dang, Stability analysis of positive switched linear systems with delays. IEEE Trans. Automat. Control 56(7), 1684–1690 (2011)MathSciNetCrossRef
11.
Zurück zum Zitat Z. Liu, X. Zhang, X. Lu, Q. Liu, Stabilization of positive switched delay systems with all subsystems unstable. Nonlinear Anal. Hybrid Syst. 29, 110–120 (2018)MathSciNetCrossRef Z. Liu, X. Zhang, X. Lu, Q. Liu, Stabilization of positive switched delay systems with all subsystems unstable. Nonlinear Anal. Hybrid Syst. 29, 110–120 (2018)MathSciNetCrossRef
12.
Zurück zum Zitat R. Ma, S. An, J. Fu, Dwell-time-based stabilization of switched positive systems with only unstable subsystem. Sci. China Inform. Sci. 64(1), 119205 (2021)MathSciNetCrossRef R. Ma, S. An, J. Fu, Dwell-time-based stabilization of switched positive systems with only unstable subsystem. Sci. China Inform. Sci. 64(1), 119205 (2021)MathSciNetCrossRef
13.
Zurück zum Zitat T. Ma, Z. Zhang, B. Cui, Variable impulsive consensus of nonlinear multi-agent systems. Nonlinear Anal. Hybrid Syst. 31, 1–18 (2019)MathSciNetCrossRef T. Ma, Z. Zhang, B. Cui, Variable impulsive consensus of nonlinear multi-agent systems. Nonlinear Anal. Hybrid Syst. 31, 1–18 (2019)MathSciNetCrossRef
14.
Zurück zum Zitat O. Mason, R. Shorten, On linear copositive lyapunov functions and the stability of switched positive linear systems. IEEE Trans. Automat. Control 52(7), 1346–1349 (2007)MathSciNetCrossRef O. Mason, R. Shorten, On linear copositive lyapunov functions and the stability of switched positive linear systems. IEEE Trans. Automat. Control 52(7), 1346–1349 (2007)MathSciNetCrossRef
15.
Zurück zum Zitat T. Mendonca, J.M. Lemos, H. Magalhães, P. Rocha, S. Esteves, Drug delivery for neuromuscular blockade with supervised multimodel adaptive control. IEEE Trans. Control Syst. Technol. 17(16), 1237–1244 (2009)CrossRef T. Mendonca, J.M. Lemos, H. Magalhães, P. Rocha, S. Esteves, Drug delivery for neuromuscular blockade with supervised multimodel adaptive control. IEEE Trans. Control Syst. Technol. 17(16), 1237–1244 (2009)CrossRef
16.
Zurück zum Zitat T. Rojsiraphisal, P. Niamsup, S. Yimnet, Global uniform asymptotic stability criteria for linear uncertain switched positive time-varying delay systems with all unstable subsystems. Mathematics 8(12), 2118 (2020)CrossRef T. Rojsiraphisal, P. Niamsup, S. Yimnet, Global uniform asymptotic stability criteria for linear uncertain switched positive time-varying delay systems with all unstable subsystems. Mathematics 8(12), 2118 (2020)CrossRef
17.
Zurück zum Zitat Y. Sun, Y. Tian, X. Xie, Stabilization of positive switched linear systems and its application in consensus of multi-agent systems. IEEE Trans. Automat. Control 62, 6608–6613 (2017)MathSciNetCrossRef Y. Sun, Y. Tian, X. Xie, Stabilization of positive switched linear systems and its application in consensus of multi-agent systems. IEEE Trans. Automat. Control 62, 6608–6613 (2017)MathSciNetCrossRef
18.
Zurück zum Zitat D. Tian, S. Liu, Y. Sun, J. Xia, Reachable set estimation for switched positive systems with mixed time?varying delays and bounded disturbances. IET Control Theory A. 12(15), 2003–2009 (2018)MathSciNetCrossRef D. Tian, S. Liu, Y. Sun, J. Xia, Reachable set estimation for switched positive systems with mixed time?varying delays and bounded disturbances. IET Control Theory A. 12(15), 2003–2009 (2018)MathSciNetCrossRef
19.
Zurück zum Zitat Y. Wang, X. Sun, F. Mazenc, Stability of switched nonlinear systems with delay and disturbance. Automatica 69, 78–86 (2016)MathSciNetCrossRef Y. Wang, X. Sun, F. Mazenc, Stability of switched nonlinear systems with delay and disturbance. Automatica 69, 78–86 (2016)MathSciNetCrossRef
20.
Zurück zum Zitat G. Wen, W.X. Zheng, On constructing multiple Lyapunov functions for tracking control of multiple agents with switching topologies. IEEE Trans. Automat. Control 64(9), 3796–3803 (2018)MathSciNetCrossRef G. Wen, W.X. Zheng, On constructing multiple Lyapunov functions for tracking control of multiple agents with switching topologies. IEEE Trans. Automat. Control 64(9), 3796–3803 (2018)MathSciNetCrossRef
21.
Zurück zum Zitat W. Xiang, J. Lam, J. Shen, Stability analysis and \(L_1\)-gain characterization for switched positive systems under dwell-time constraint. Autmatica 85, 1–8 (2017)CrossRef W. Xiang, J. Lam, J. Shen, Stability analysis and \(L_1\)-gain characterization for switched positive systems under dwell-time constraint. Autmatica 85, 1–8 (2017)CrossRef
22.
Zurück zum Zitat M.B. Yazdi, M.R. Jahed-Motlagh, Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization. Chem. Eng. J. 155(3), 838–843 (2009)CrossRef M.B. Yazdi, M.R. Jahed-Motlagh, Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization. Chem. Eng. J. 155(3), 838–843 (2009)CrossRef
23.
Zurück zum Zitat Y. Yin, G. Zong, X. Zhao, Improved stability criteria for switched positive linear systems with average dwell time switching. J. Franklin Inst. 354, 3472–3484 (2017)MathSciNetCrossRef Y. Yin, G. Zong, X. Zhao, Improved stability criteria for switched positive linear systems with average dwell time switching. J. Franklin Inst. 354, 3472–3484 (2017)MathSciNetCrossRef
24.
Zurück zum Zitat J. Zhang, Z. Han, F. Zhu, J. Huang, Stability and stabilization of positive switched systems with mode-dependent average dwell time. Nonlinear Anal. Hybrid Syst. 9, 42–55 (2013)MathSciNetCrossRef J. Zhang, Z. Han, F. Zhu, J. Huang, Stability and stabilization of positive switched systems with mode-dependent average dwell time. Nonlinear Anal. Hybrid Syst. 9, 42–55 (2013)MathSciNetCrossRef
25.
Zurück zum Zitat J. Zhang, Y. Sun, Reachable set estimation for switched nonlinear positive systems with impulse and time delay. Int. J. Robust Nonlinear Control 30, 3332–3343 (2020)MathSciNetCrossRef J. Zhang, Y. Sun, Reachable set estimation for switched nonlinear positive systems with impulse and time delay. Int. J. Robust Nonlinear Control 30, 3332–3343 (2020)MathSciNetCrossRef
26.
Zurück zum Zitat X. Zhao, X. Liu, S. Yin, H. Li, Improved results on stability of continuous-time switched positive linear systems. Automatica 50(2), 614–621 (2014)MathSciNetCrossRef X. Zhao, X. Liu, S. Yin, H. Li, Improved results on stability of continuous-time switched positive linear systems. Automatica 50(2), 614–621 (2014)MathSciNetCrossRef
27.
Zurück zum Zitat X. Zhao, Y. Yin, L. Liu, X. Sun, Stability analysis and delay control for switched positive linear systems. IEEE Trans. Automat. Control 63(7), 2184–2190 (2017)MathSciNetCrossRef X. Zhao, Y. Yin, L. Liu, X. Sun, Stability analysis and delay control for switched positive linear systems. IEEE Trans. Automat. Control 63(7), 2184–2190 (2017)MathSciNetCrossRef
28.
Zurück zum Zitat X. Zhao, L. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)MathSciNetCrossRef X. Zhao, L. Zhang, P. Shi, M. Liu, Stability of switched positive linear systems with average dwell time switching. Automatica 48(6), 1132–1137 (2012)MathSciNetCrossRef
Metadaten
Titel
Practical Exponential Stability of Positive Switched Linear System and Its Application in Practical Consensus of Multi-agent System
verfasst von
Yanhao Ju
Fanwei Meng
Yuangong Sun
Publikationsdatum
23.08.2024
Verlag
Springer US
Erschienen in
Circuits, Systems, and Signal Processing / Ausgabe 12/2024
Print ISSN: 0278-081X
Elektronische ISSN: 1531-5878
DOI
https://doi.org/10.1007/s00034-024-02771-6