Constructive stability and stabilizability of positive linear discrete-time switching systems
We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. The systems constituting this class can be treated as a natural generalization of systems with the so-called independently switching state vector components. Distinctive feature of such systems is that their components can be arbitrarily “re-connected” in parallel or in series without loss of the “constructive resolvability” property for the problems of stability or stabilizability of a system. It is shown also that, for such systems, the individual positive trajectories with the greatest or the lowest rate of convergence to the zero can be built constructively.
Keywordsswitching systems stability stabilizability constructive criteria Hourglass alternative
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- 5.V. Kozyakin, “A short introduction to asynchronous systems,” in Proc. 6th Int. Conf. on Difference Equations, Boca Raton, FL, 2004 (CRC, Boca Raton, 2004), pp. 153–165.Google Scholar
- 10.J. Theys, “Joint spectral radius: Theory and approximations,” Ph. D. Dissertation, Faculté des sciences appliquées, Département d’ingénierie mathématique, Center for Systems Engineering and Applied Mechanics, Univ. Catholique de Louvain (May 2005).Google Scholar
- 11.R. Jungers, “The joint spectral radius,” in Lecture Notes in Control and Information Sciences, Vol. 385: Theory and Applications (Springer-Verlag, Berlin, 2009).Google Scholar
- 15.V. D. Blondel, J. Theys, and A. A. Vladimirov, “Switched systems that are periodically stable may be unstable,” in Proc. 15th Int. Symp. on Math. Theory of Networks and Systems (MTNS), Notre-Dame, USA, Aug. 12—16, 2002 (Univ. Notre-Dame, 2002).Google Scholar
- 16.V. Kozyakin, “A dynamical systems construction of a counterexample to the finiteness conjecture,” in Proc. 44th IEEE Conf. on Decision and Control, 2005 and 2005 Eur. Control Conf. CDCECC’05, 2005 (IEEE, New York, 2005), pp. 2338–2343.Google Scholar