Abstract
In the paper, the k-switching reachability set R k of a continuous-time positive switched system is introduced, and a necessary and sufficient condition for the chain of this sets {R k , k ∈ ℕ} to stop increasing after some finite index k is given. It is shown that, for special classes of (multiple-input) positive switched systems, reachability always ensures that \({\bf R}_n = \mathbb{R}_+^n\), n being the system dimension.
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References
Farina, L., Rinaldi, S.: Positive linear systems: theory and applications. Series on Pure and Applied Mathematics. Wiley-Interscience, New York (2000)
Mason, O., Shorten, R.N.: Some results on the stability of positive switched linear systems. In: Proceedings of the 43rd Conference on Decision and Control, Paradise Island, Bahamas, pp. 4601–4606 (2004)
Mason, O., Shorten, R.N.: On linear copositive Lyapunov functions and the stability of switched positive linear systems. IEEE Transactions on Automatic Control 52, 1346–1349 (2007)
Santesso, P., Valcher, M.E.: An algebraic approach to the structural properties of continuous time positive switched systems. In: Commault, C., Marchand, N. (eds.) LNCIS, pp. 185–192. Springer, Heidelberg (2006)
Santesso, P., Valcher, M.E.: Controllability and reachability of switched positive systems. In: Proceedings of the Seventeenth International Symposium on Mathematical Theory of Networks and Systems, Kyoto, Japan (2006); File MoP01.3.pdf
Valcher, M.E.: On the k-switching reachability sets of single-input positive switched systems. Submitted to the 2009 American Control Conference, St. Louis (2009)
Valcher, M.E., Santesso, P.: On the reachability of single-input positive switched systems. In: Proceedings of the 47th Conference on Decision and Control, Cancun, Mexico, pp. 947–952 (2008)
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Valcher, M.E. (2009). k-Switching Reachability Sets of Continuous-Time Positive Switched Systems. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_17
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DOI: https://doi.org/10.1007/978-3-642-02894-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02893-9
Online ISBN: 978-3-642-02894-6
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