Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The asymptotic stability of positive switched linear systems for any switchings is addressed. Simple sufficient conditions for the asymptotic stability of positive switched continuous-time and discrete-time linear systems are established. It is shown that the positive switched continuous-time (discrete-time) system is asymptotically stable for any switchings if the sum of entries of every column of the matrices of subsystems is negative (less than 1)

Słowa kluczowe

EN

positive; linear; switched system; asymptotic stability; sufficient conditions

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2013
• Tom: Vol. 61, nr 2
• Strony: 343--347
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland

Bibliografia

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• [5] L. Gurvits, R. Shorten, and O. Mason, “On the stability of switched positive linear systems”, IEEE Trans. Autom. Control. 52, 1099-1103 (2007).
• [6] T. Kaczorek, Positive 1D and 2D Systems, Springer Verlag, London, 2002.
• [7] T. Kaczorek, “Positive switched 2D linear systems described by the Roesser models”, Proc. 19th Int. Symp. Math. Theoryof Network and Systems 1, CD-ROM (2012).
• [8] T. Kaczorek, “Positive switched 2D linear systems described by general model”, Acta Mechanica et Automatica 4, 36-41 (2010).
• [9] T. Kaczorek, “Choice of the forms of Lyapunov functions for 2D Roesser model”, Int. J. Apply. Math. and Comp. Sci. 17, 471-475 (2007).
• [10] D. Liberzon, Switching in System and Control, Birklauser, Berlin, 2003.
• [11] X.W. Liu, “Stability analysis of switched positive systems: a switched linear copositive Lyapunov function method”, IEEETrans. Circ. Sys. II, Express Brief 56, 414-418 (2009).
• [12] X.W. Liu, L. Wang, W.S. Yu, and S.M. Zhong, “Constrained control of positive discrete-time systems with delays”, IEEETrans. Circ. Sys. II, Express Brief 55, 193-197 (2008).
• [13] X.W. Liu and C.Y. Dang, “Stability analysis of positive switched linear systems with delays”, IEEE Trans. Autom. Control 56, 1684-1690 (2011).
• [14] O. Mason and R. Shorten, “On linear copositive Lyapunov functions and the stability of switched positive linear systems”, IEEE Trans. Autom. Control 52, 1346-1349 (2007).
• [15] R.S. Varga, Matrix Interactive Analysis, Springer-Verlag, Berlin, 2002.
• [16] X.D. Zhao, L.X. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching”, Automatica 48, 1132-1137 (2012).