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This article is cited in 2 scientific papers (total in 2 papers)
Control processes
A Lyapunov matrix based stability criterion for a class of time-delay systems
M. Gomeza, A. V. Egorovb, S. Mondiéa a CINVESTAV-IPN, 2508, Av. Instituto Politécnico Nacional, Mexico city,
07360, United Mexican States
b St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg,
199034, Russian Federation
Abstract:
This paper is devoted to the stability analysis of linear time-invariant systems with multiple delays. First, we recover some basic elements of our research. Namely, we introduce the complete type functionals, the delay Lyapunov matrix, and a space of special functions that allow to present a family of necessary stability conditions. Then, we prove a sufficient stability condition (instability condition) in terms of a quadratic Lyapunov–Krasovskii functional. Summarizing these results, we finally obtain an exponential stability criterion for a class of linear time-delay systems. The criterion requires only a finite number of mathematical operations to be tested and depends uniquely on the delay Lyapunov matrix. Refs 15.
Keywords:
time-delay system, Lyapunov matrix, stability criterion.
Received: September 2, 2017 Accepted: October 12, 2017
Citation:
M. Gomez, A. V. Egorov, S. Mondié, “A Lyapunov matrix based stability criterion for a class of time-delay systems”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 13:4 (2017), 407–416
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https://www.mathnet.ru/eng/vspui349 https://www.mathnet.ru/eng/vspui/v13/i4/p407
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Abstract page: | 170 | Full-text PDF : | 34 | References: | 33 | First page: | 13 |
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