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Constructive stability and stabilizability of positive linear discrete-time switching systems

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Abstract

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.

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Correspondence to V. S. Kozyakin.

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Published in Russian in Informatsionnye Protsessy, 2016, Vol. 16, No. 2, pp. 194–206.

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Kozyakin, V.S. Constructive stability and stabilizability of positive linear discrete-time switching systems. J. Commun. Technol. Electron. 62, 686–693 (2017). https://doi.org/10.1134/S1064226917060110

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  • DOI: https://doi.org/10.1134/S1064226917060110

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