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.
Citation:
Rinat A. Kamalov, Vladimir Yu. Protasov, “On the Length of Switching Intervals of a Stable Dynamical System”, Optimal Control and Dynamical Systems, Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze, Trudy Mat. Inst. Steklova, 321, Steklov Math. Inst., Moscow, 2023, 162–171; Proc. Steklov Inst. Math., 321 (2023), 149–157
\Bibitem{KamPro23}
\by Rinat~A.~Kamalov, Vladimir~Yu.~Protasov
\paper On the Length of Switching Intervals of a Stable Dynamical System
\inbook Optimal Control and Dynamical Systems
\bookinfo Collected papers. On the occasion of the 95th birthday of Academician Revaz Valerianovich Gamkrelidze
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 321
\pages 162--171
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4313}
\crossref{https://doi.org/10.4213/tm4313}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 321
\pages 149--157
\crossref{https://doi.org/10.1134/S0081543823020116}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85170839630}