Razumikhin approach in the generalized Myshkis problem for systems with distributed delay
DOI:
https://doi.org/10.21638/11701/spbu10.2023.202Abstract
The paper gives sufficient conditions for the solvability of the generalized Myshkis problem for a system of equations with a distributed time-varying delay and a constant kernel. Conditions on the kernel which guarantee the uniform stability of the system for any admissible delay are obtained. The admissible delay in this paper is a piecewise continuous function bounded from above in magnitude and growth rate. The applicability of the obtained conditions is illustrated by two examples.
Keywords:
time-delay system, stability, distributed delay, generalized Myshkis problem, Razumikhin approach
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Литература
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References
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Malygina V. V. O tochnykh granitsakh oblasti ustoichivosti lineinykh differentsial'nykh uravnenii s raspredelennym zapazdyvaniem [On the exact boundaries of the stability domain of linear differential equations with distributed delay]. Izvestiia vysshikh uchebnykh zavedenii. Matematika [ Russian Mathematics ], 2008, iss. 52, no. 7, pp. 15-23. (In Russian)
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Egorov A. The generalized Myshkis problem for a linear time-delay system with time-varying delay. Stability and Control Processes (SCP 2020), Lecture Notes in Control and Information Sciences - Proceedings. Eds N. Smirnov, A. Golovkina. Cham, Switzerland, Springer Publ., 2022, pp. 223-231.
Egorov A. Robust stability analysis of time-varying delay systems. 17th IFAC Workshop on Time Delay Systems. Montreal, Canada, 2022, pp. 210-215.
Fridman E. An improved stabilization method for linear time-delay systems. IEEE Transactions on Automatic Control, 2002, vol. 47, no. 11, pp. 1931-1937.
Wu M., He Y., She J.-H., Liu G.-P. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 2004, vol. 40, pp. 1435-1439.
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Published
2023-07-27
How to Cite
Egorov, A. V. (2023). Razumikhin approach in the generalized Myshkis problem for systems with distributed delay. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19(2), 148–161. https://doi.org/10.21638/11701/spbu10.2023.202
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Applied Mathematics
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Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
