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On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays

Authors: Xiuyong Ding, Shouming Zhong, Xiu Liu


This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Switched Systems, delays, Common linear co-positive Lyapunov functions, positive systems

Digital Object Identifier (DOI):

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[1] A. Berman, M. Neumann, and R. Stern, Nonnegative matrices in dynamic systems, New York: Wiley, 1989.
[2] T. Kaczorek, Positive 1D and 2D Systems, London: Springer-Verlag, 2002.
[3] L. Benvenuti, A. D. Santis, and L. Farina(Eds.), Positive Systems, Berlin, Germany: Springer-Verlag, 2003.
[4] L. Farina and S. Rinaldi, Positive linear systems: theory and applications, New York: Wiley, 2000.
[5] A. Jadbabaie, J. Lin, and A. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Transaction on Automatic Control, vol. 48, pp. 988-1001, 2003.
[6] X. Liu, "Stability Analysis of Switched Positive Systems: A Switched Linear Copositive Lyapunov Function Method," IEEE Transaction on Circuits and Systtems II, vol. 56, no. 5, pp. 414-418, 2009.
[7] M. A. Rami and F. Tadeo, "Controller synthesis for positive linear systems with bounded controls," IEEE Transaction on Circuits and systems II, vol. 54, no. 2, pp. 151-155, 2007.
[8] R. Shorten, D. Leith, J. Foy, and R. Kilduff, "Towards an analysis and design framework for congestion control in communication networks," in: Proceedings of the 12th Yale Workshop on Adaptive and Learning Systems, 2003.
[9] X. Liu, "Stability Analysis of Positive Systems With Bounded Time- Varying Delays," IEEE Transaction on Circuits and Systtems II, vol. 56, no. 7, pp. 600-604, 2009.
[10] R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King, "Stability Theory for Switched and Hybrid Systems, SIAM Review vol. 49, no. 4, pp. 545- 592, 2007
[11] O. Mason and R. Shorten, "A conjecture on the existence of common quadratic Lyapunov functions for positive linear systems, in: Proceedings of the 2003 American Control Conference, New York City, USA, 2003.
[12] L. Gurvits, R. Shorten, and O. Mason, "On the stability of switched positive linear systems," IEEE Transaction on Automatic Control, vol. 52, no. 6, pp. 1099-1103, 2007.
[13] O. Mason and R. Shorten, "On the simultaneous diagonal stability of pair of positive linear systems, Linear Algebra and its Application, vol. 413 no. 1, pp. 13-23, 2006.
[14] O. Mason and R. Shorten, "On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems," IEEE Transaction on Automatic Control, vol. 52, no. 7, pp. 1346-1349, 2007.
[15] X. Ding, L. Shu, and Z. Wang, "On stability for switched linear positive systems," Mathematical and Computer Modelling, vol. 53, pp. 1044- 1055, 2011.
[16] R. T. Rockafellar, Convex Analysis, Princeton, NJ, USA: Prinnceton University Press, 1970.
[17] R. Horn, C. Johnson, "Topics in matrix analysis, Cambridge University Press, 1991.