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Języki publikacji
Abstrakty
Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that All convex combinations of the system matrices are Hurwitz, becomes equivalent to the generally weaker condition that the systems matrices are Hurwitz. In the special case of two-dimensional systems, this allows for drawing a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated.
Czasopismo
Rocznik
Tom
Strony
47--62
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Dipartimento di Ingegneria dell’Informazione, Universitá di Padova, via Gradenigo 6/B, 35131 Padova, Italy
autor
- Dipartimento di Ingegneria dell’Informazione, Universitá di Padova, via Gradenigo 6/B, 35131 Padova, Italy
Bibliografia
- 1. Akar, M., Paul, A., Safonov, M.G. and Mitra, U. (2006) Conditions on the stability of a class of second order switched systems. IEEE Trans. Aut. Contr., 51, 338–340.
- 2. Aliprantis, C.D. and Tourky, R. (2007) Cones and Duality. American Mathematical Society.
- 3. Barabanov, N.E. (1988) Absolute characteristic exponent of a class of linear nonstationary systems of differential equations. Siberian Math. J., 29, 521–530.
- 4. Berman, A. and Plemmons, R.J. (1979) Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (NY).
- 5. Blanchini, F., Colaneri, P. and Valcher, M.E. (2011) Is stabilization of switched positive linear systems equivalent to the existence of a Hurwitz convex combination of the system matrices? In: Proceedings of the 50th IEEE CDC. IEEE Orlando, FL, 1834 – 1839.
- 6. Blanchini, F., Colaneri, P. and Valcher, M.E. (2012) Co-positive Lyapunov functions for the stabilization of positive switched systems. IEEE Trans.Aut. Contr., DOI 10.1109/TAC.2012.2199169.
- 7. Fainshil, L., Margaliot, M. and Chigansky, P. (2009) On the stability of positive linear switched systems under arbitrary switching laws. IEEE Trans. Automat. Control, 54, 807–899.
- 8. Farina, L. and Rinaldi, S. (2000) Positive linear Systems: Theory and Applications. Wiley-Interscience, Series on Pure and Applied Mathematics, New York.
- 9. Fornasini, E. and Valcher, M.E. (2010) Linear copositive Lyapunov functions for continuous-time positive switched systems. IEEE Trans. Aut. Contr., 55 (8), 1933–1937.
- 10. Gurvits, L., Shorten, R. and Mason, O. (2007) On the stability of switched positive linear systems. IEEE Trans. on Aut. Contr., 52 (6),1099–1103.
- 11. Horn, R.A. and Johnson, C.R. (1991) Topics in Matrix Analysis. Cambridge University Press, Cambridge.
- 12. Kaczorek, T. (2002) Positive 1D and 2D systems. Springer Verlag, London.
- 13. King, C. and Nathanson, M. (2006) On the existence of common quadratic Lyapunov functions for a rank one difference. Linear Algebra and its Appl., 419, 400–416.
- 14. Knorn, F., Mason, O. and Shorten, R.N. (2009) On linear co-positive Lyapunov functions for sets of linear positive systems. Automatica, 45 (8), 1943–1947.
- 15. Mason, O. and Shorten, R.N. (2004) Some results on the stability of positive switched linear systems. In Proceedings of the 43rd Conference on Decision and Control (CDC 2004), Paradise Island, Bahamas, 4601–4606.
- 16. Mason, O. and Shorten, R.N. (2007a) On linear copositive Lyapunov functions and the stability of switched positive linear systems. IEEE Trans. on Aut. Contr., 52 (7), 1346 – 1349.
- 17. Mason, O. and Shorten, R.N. (2007b) Quadratic and copositive Lyapunov functions and the stability of positive switched linear systems. In: Proceedings of the American Control Conference (ACC 2007), New York. IEEE, 657–662.
- 18. Shorten, R., Corless., M., Wulff, K., Klinge, S. and Middleton, R. (2009) Quadratic stability and singular SISO switching systems. IEEE Trans. Aut. Contr., 54 (11), 2714–2718.
- 19. Shorten, R., Mason, O., O’cairbre, F. and Curran, P. (2004) A unifying framework for the SISO circle criterion and other quadratic stability criteria. Int. J. Contr., 77 (1), 1–8.
- 20. Shorten, R., Wirth, F., Mason, O., Wulff, K., and King, C. (2007) Stability criteria for switched and hybrid systems. SIAM Review, 49, 545–592.
- 21. Zappavigna , A., Colaneri, P., Jeromel, J.C., and Middleton, R. (2010) Stabilization of continuous-time switched linear positive systems. In Proceedings of the 2010 American Control Conference, Baltimore, MD. IEEE, 3275–3280.
Typ dokumentu
Bibliografia
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