On General Stability for Switched Positive Linear Systems with Bounded Time-varying Delays
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331167Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1088
 A. Berman, M. Neumann, and R. Stern, Nonnegative matrices in dynamic systems, New York: Wiley, 1989.
 T. Kaczorek, Positive 1D and 2D Systems, London: Springer-Verlag, 2002.
 L. Benvenuti, A. D. Santis, and L. Farina(Eds.), Positive Systems, Berlin, Germany: Springer-Verlag, 2003.
 L. Farina and S. Rinaldi, Positive linear systems: theory and applications, New York: Wiley, 2000.
 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.
 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.
 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.
 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.
 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.
 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
 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.
 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.
 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.
 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.
 X. Ding, L. Shu, and Z. Wang, "On stability for switched linear positive systems," Mathematical and Computer Modelling, vol. 53, pp. 1044- 1055, 2011.
 R. T. Rockafellar, Convex Analysis, Princeton, NJ, USA: Prinnceton University Press, 1970.
 R. Horn, C. Johnson, "Topics in matrix analysis, Cambridge University Press, 1991.