Geodesic
On the Length of Switching Intervals of a Stable Dynamical System
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 162-171

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A linear switching system is a system of linear ODEs with time-dependent matrix taking values in a given control matrix set. The system is asymptotically stable if all its trajectories tend to zero for every control matrix function. Mode-dependent restrictions on the lengths of switching intervals can be imposed. Does the system remain stable after removal of the restrictions? When does the stability of the trajectories with short switching intervals imply the stability of all trajectories? The answers to these questions are given in terms of the “tail cut-off points” of linear operators. We derive an algorithm to compute them by applying Chebyshev-type exponential polynomials.
Keywords: linear switching system, dynamical system, stability, switching time intervals, extremal polynomial, Chebyshev system, convex extremal problem.
Mots-clés : quasipolynomials 
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     title = {On the {Length} of {Switching} {Intervals} of a {Stable} {Dynamical} {System}},
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Rinat A. Kamalov; Vladimir Yu. Protasov. On the Length of Switching Intervals of a Stable Dynamical System. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Dynamical Systems, Tome 321 (2023), pp. 162-171. http://geodesic.mathdoc.fr/item/TM_2023_321_a10/