Asymptotic stability and stabilizability of special classes of discrete-time positive switched systems

Linear Algebra and Its Applications

Volumn 438, Issue 4, 2013, Pages 1814-1831

  Fornasini, Ettore ^a   Valcher, Maria Elena ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

(Global uniform) asymptotic stability; Circulant matrix; Monomial matrix; Positive linear system; Stabilizability; Switched system

Indexed keywords

CIRCULANT MATRIX; MONOMIAL MATRICES; POSITIVE LINEAR SYSTEMS; STABILIZABILITY; SWITCHED SYSTEM;

ASYMPTOTIC STABILITY; LINEAR SYSTEMS;

SWITCHING SYSTEMS;

EID: 84872109356     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2011.08.028     Document Type: Conference Paper

References (34)

1. C.D. Aliprantis, and R. Tourky Cones and Duality 2007 American Mathematical Society
2. M. Araki Application of M-matrices to the stability problems of composite dynamical systems J. Math. Anal. Appl. 52 1975 309 321
3. V.D. Blondel, J. Theys, and A.A. Vladimirov An elementary counterexample to the finiteness conjecture SIAM J. Matrix Anal. Appl. 24 2003 963 970
4. T. Bousch, and J. Mairesse Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture J. Amer. Math. Soc. 15 2001 77 111
5. R.A. Brualdi, and H.J. Ryser Combinatorial Matrix Theory 1991 Cambridge University Press Cambridge (GB)
6. I. Daubechies, and J.C. Lagarias Sets of matrices all infinite products of which converge Linear Algebra Appl. 161 1992 227 263
7. P.J. Davis Circulant Matrices 1979 John Wiley & Sons New York
8. H.G. Eggleston Convexity Cambridge Tracts in Mathematics and Mathematical Physics vol. 47 1958 Cambridge University Press Cambridge, UK
9. L. Farina, and S. Rinaldi Positive Linear Systems: Theory and Applications 2000 Wiley-Interscience, Series on Pure and Applied Mathematics New York
10. E. Fornasini, and M.E. Valcher Linear copositive Lyapunov functions for continuous-time positive switched systems IEEE Trans. Automat. Control 55 8 2010 1933 1937
11. E. Fornasini, M.E. Valcher, Stabilizability of discrete-time positive switched systems, in: Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, 2010, pp. 432-437.
12. J.C. Geromel, and P. Colaneri Stability and stabilization of discrete time switched systems Internat. J. Control 79 7 2006 719 728
13. L. Gurvits Stability of discrete linear inclusions Linear Algebra Appl. 231 1995 47 85
14. L. Gurvits, R. Shorten, and O. Mason On the stability of switched positive linear systems IEEE Trans. Automat. Control 52 6 2007 1099 1103
15. E. Hernandez-Varga, R. Middleton, P. Colaneri, and F. Blanchini Discrete-time control for switched positive systems with application to mitigating viral escape Internat. J. Robust Nonlinear Control 2010 10.1002/rnc.1628
16. R.A. Horn, and C.R. Johnson Topics in Matrix Analysis 1991 Cambridge University Press Cambridge (UK)
17. Y. Huang, J. Luo, T. Huang, and M. Xiao The set of stable switching sequences for discrete-time linear switched systems J. Math. Anal. Appl. 377 2011 732 743
18. A. Jadbabaie, J. Lin, and A.S. Morse Coordination of groups of mobile autonomous agents using nearest neighbor rules IEEE Trans. Automat. Control 48 6 2003 988 1001
19. R. Jungers The joint spectral radius: theory and applications Lecture Notes in Control and Information Sciences vol. 385 2009 Springer
20. 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
21. J.C. Lagarias, and Y. Wang The finiteness conjecture for the generalized spectral radius of a set of matrices Linear Algebra Appl. 214 1995 17 42
22. J.-W. Lee, and G.E. Dullerud Optimal disturbance attenuation for discrete-time switched and markovian jump linear systems SIAM J. Control Optim. 45 4 2006 1329 1358
23. J.-W. Lee, and G.E. Dullerud Uniform stabilization of discrete-time switched and markovian jump linear systems Automatica 42 2006 205 218
24. D. Liberzon Switching in Systems and Control Volume in Series Systems and Control: Foundations and Applications 2003 Birkhauser Boston (MA)
25. O. Mason, and R.N. Shorten On common quadratic Lyapunov functions for stable discrete-time LTI systems IMA J. Appl. Math. 69 2004 271 283
26. O. Mason, and R.N. Shorten Some results on the stability of positive switched linear systems dsdf Proceedings of the 43rd Conference on Decision and Control (CDC 2004) 2004 Paradise Island Bahamas 4601 4606
27. O. Mason, and R.N. Shorten On linear copositive Lyapunov functions and the stability of switched positive linear systems IEEE Trans. Automat. Control 52 7 2007 1346 1349
28. O. Mason, and R.N. Shorten Quadratic and copostive Lyapunov functions and the stability of positive switched linear systems Proceedings of the American Control Conference (ACC 2007), New York 2007 657 662
29. T. Monovich, and M. Margaliot Analysis of discrete-time linear switched systems: a variational approach SIAM J. Control Optim. 49 2011 808 829
30. T. Monovich, and M. Margaliot A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems Automatica 47 2011 1489 1495
31. O. Rojo, and R.L. Soto Guo perturbation for symmetric nonnegative circulant matrices Linear Algebra Appl. 431 2009 594 607
32. A. Salomaa, and M. Soittola Automata Theoretic Aspects of Formal Power Series 1978 Springer-Verlag
33. R. Shorten, F. Wirth, and D. Leith A positive systems model of TCP-like congestion control: asymptotic results IEEE/ACM Trans. Networking 14 3 2006 616 629
34. W. Zhang, A. Abate, J. Hu, and M.P. Vitus Exponential stabilization of discrete-time switched linear systems Automatica 45 2009 2526 2536