Abstract
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.
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The authors are grateful to the anonymous referee for the careful reading and many valuable comments.
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This work is supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS.”
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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Vol. 321, pp. 162–171 https://doi.org/10.4213/tm4313.
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Kamalov, R.A., Protasov, V.Y. On the Length of Switching Intervals of a Stable Dynamical System. Proc. Steklov Inst. Math. 321, 149–157 (2023). https://doi.org/10.1134/S0081543823020116
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DOI: https://doi.org/10.1134/S0081543823020116