Stability of switched positive linear systems with average dwell time switching

Automatica

Volumn 48, Issue 6, 2012, Pages 1132-1137

  Zhao, Xudong ^a   Zhang, Lixian ^b   Shi, Peng ^c,d   Liu, Ming ^b  

^a CHINA UNIVERSITY OF PETROLEUM   (China)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

^c UNIVERSITY OF GLAMORGAN   (United Kingdom)

^d VICTORIA UNIVERSITY   (Australia)

Author keywords

Average dwell time; Multiple linear copositive Lyapunov function; Stability; Switched positive linear systems

Indexed keywords

ARBITRARY SWITCHING; AVERAGE DWELL TIME; CONTINUOUS TIME; COPOSITIVE; NUMERICAL EXAMPLE; POSITIVE LINEAR SYSTEMS; STABILITY ANALYSIS; STABILITY RESULTS; UNDERLYING SYSTEMS;

CONVERGENCE OF NUMERICAL METHODS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NUMERICAL ANALYSIS; STABILITY CRITERIA; SWITCHING SYSTEMS;

SWITCHING;

EID: 84860315302     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2012.03.008     Document Type: Article

References (34)

1. L. Benvenuti, and L. Farina A tutorial on the positive realization problem IEEE Transactions on Automatic Control 49 5 2004 651 664
2. C. Cui, F. Long, and C. Li Disturbance attenuation for switched system with continuous-time and discrete-time subsystems: state feedback case ICIC Express Letters 4 1 2010 205 212
3. P. De Leenheer, and D. Aeyels Stabilization of positive linear systems Systems & Control Letters 44 4 2001 259 271 (Pubitemid 33018678)
4. X. Ding, L. Shu, and X. Liu On linear copositive Lyapunov functions for switched positive systems Journal of the Franklin Institute 348 2011 2099 2107
5. L. Fainshil, M. Margaliot, and P. Chigansky On the stability of positive linear switched systems under arbitrary switching laws IEEE Transactions on Automatic Control 54 4 2009 897 899
6. L. Farina, and S. Rinaldi Positive linear systems 2000 Wiley Interscience Series New York
7. J. Feng, J. Lam, P. Li, and Z. Shu Decay rate constrained stabilization of positive systems using static output feedback International Journal of Robust and Nonlinear Control 21 2011 44 54
8. E. Fornasini, and M.E. Valcher Linear copositive Lyapunov functions for continuous-time positive switched systems IEEE Transactions on Automatic Control 55 8 2010 1933 1937
9. L. Gurvits, R. Shorten, and O. Mason On the stability of switched positive linear systems IEEE Transactions on Automatic Control 52 6 2007 1099 1103 (Pubitemid 47034040)
10. A. Jadbabaie, J. Lin, and A.S. Morse Co-ordination of groups of mobile autonomous agents using nearest neighbor rules IEEE Transactions on Automatic Control 48 6 2003 988 1001
11. T. Kaczorek Positive 1D and 2D systems 2002 Springer Verlag London
12. F. Knorn, O. Mason, and R.N. Shorten On linear co-positive Lyapunov functions for sets of linear positive systems Automatica 45 8 2009 1943 1947
13. D. Liberzon Switching in systems and control 2003 Birkhauser Berlin
14. P. Li, J. Lam, Z. Wang, and P. Date Positivity-preserving H∞ model reduction for positive systems Automatica 47 7 2011 1504 1511
15. H. Lin, and P.J. Antsaklis Stability and stabilizability of switched linear systems: a survey of recent results IEEE Transactions on Automatic Control 54 2 2009 308 322
16. X. Liu, and C. Dang Stability analysis of positive switched linear systems with delays IEEE Transactions on Automatic Control 56 7 2011 1684 1690
17. M. Margaliot, and M.S. Branicky Nice reachability for planar bilinear control systems with applications to planar linear switched systems IEEE Transactions on Automatic Control 54 4 2009 900 905
18. Mason, O., & Shorten, R. (2003). A conjecture on the existence of common quadratic Lyapunov functions for positive linear systems. In Proc. ameri. contr. conf. (pp. 4469-4470).
19. Mason, O., & Shorten, R. (2004). Some results on the stability of positive switched linear systems. In Proc. of the 43rd IEEE conference on decision and control (pp. 4601-4606). Atlantis, Bahamas. (Pubitemid 40307750)
20. O. Mason, and R. Shorten On linear copositive Lyapunov functions and the stability of switched positive linear systems IEEE Transactions on Automatic Control 52 7 2007 1346 1349 (Pubitemid 47098951)
21. M.A. Rami Solvability of static output-feedback stabilization for LTI positive systems Systems & Control Letters 60 2011 704 708
22. P. Shi, Y. Xia, G. Liu, and D. Rees On designing of sliding mode control for stochastic jump systems IEEE Transactions on Automatic Control 51 1 2006 97 103 (Pubitemid 43137935)
23. X. Sun, W. Wang, G. Liu, and J. Zhao Stability analysis for linear switched systems with time-varying delay IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 38 2 2008 528 533 (Pubitemid 351479570)
24. L 2-gain analysis for switched delay systems: a delay-dependent method Automatica 42 10 2006 1769 1774 (Pubitemid 44277968)
25. D. Wang, W. Wang, and P. Shi Delay-dependent exponential stability for switched delay systems Optimal Control Applications and Methods 30 4 2009 383 397
26. D. Wang, W. Wang, and P. Shi Exponential H∞ filtering for switched linear systems with interval time-varying delay International Journal of Robust and Nonlinear Control 19 5 2009 532 551
27. S. Xu, and T. Chen Robust H∞ control for uncertain discrete-time stochastic bilinear systems with Markovian switching International Journal of Robust and Nonlinear Control 15 5 2005 201 217 (Pubitemid 40384287)
28. X. Xue, and Z. Li Asymptotic stability analysis of a kind of switched positive linear discrete systems IEEE Transactions on Automatic Control 55 9 2010 2198 2203
29. G. Zhai, I. Matsune, J. Imae, and T. Kobayashi A note on multiple Lyapunov functions and stability condition for switched and hybrid systems Int. J. Innovative Computing, Information and Control 5 5 2009 1189 1200
30. L. Zhang, and H. Gao Asynchronously switched control of switched linear systems with average dwell time Automatica 46 5 2010 953 958
31. L. Zhang, and B. Jiang Stability of a class of switched linear systems with uncertainties and average dwell time switching Int. J. Innovative Computing, Information and Control 6 2 2010 667 676
32. l 2-gain and asynchronous H∞ control of discrete-time switched systems with average dwell time IEEE Transactions on Automatic Control 54 9 2009 2193 2200
33. L 2-gain and H∞ control for switched systems Automatica 44 5 2008 1220 1232
34. X. Zhao, and Q. Zeng Delay-dependent H∞ performance analysis and filtering for Markovian jump systems with interval time-varying-delays International Journal of Adaptive Control and Signal Processing 24 8 2010 633 642