Abstract
We consider linear stationary systems of differential equations with delay. The matrices that determine the dynamics of a system vary within a certain interval. We obtain sufficient conditions for the robust stability of systems uniform with respect to delay and depending on the deviation of the argument.
References
E. I. Jury, “Robustness of discrete systems. A survey,”Avtomat. Telemekh., No. 5, 3–28 (1990).
V. L. Kharitonov, “On the asymptotic stability of the equilibrium state for a family of systems of linear differential equations,”Differents. Uravn.,14, No. 11, 2086–2088 (1978).
V. L. Kharitonov, “On a generalization of the criterion of stability,”Izv. Akad. Nauk. Kaz. SSR,14, No. 11, 2086–2088 (1978).
Yu. M. Gusev, V. N. Efanov, V. G. Krymskii, and V. Yu. Rutkovskii, “Analysis and synthesis of linear interval dynamical systems (the state of the problem). Analysis of stability of interval matrices and synthesis of robust controllers,”Izv. Akad. Nauk SSSR. Tekh. Kibern., No. 2, 3–30 (1991).
J. Hale,Theory of Functional Differential Equations [Russian translation], Mir, Moscow (1984).
D. Ya. Khusainov and A. N. Sharkovskii, “Stability of solutions of differential equations with delayed argument,” in:Functional and Differential-Difference Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1974), pp. 141–147.
D. Ya. Khusainov and E. A. Yun'kova, “Estimation of the magnitude of delay in linear differential systems with deviating argument,”Ukr. Mat. Zh.,35, No. 2, 261–264 (1983).
D. Ya. Khusainov, “Exponential estimation of solutions of linear systems with delay for arbitrary deviations of the argument,”Differents. Uravn.,25, No. 9, 1631–1633 (1989).
D. G. Korenevskii,Stability of Solutions of Deterministic and Stochastic Differential-Difference Equations [in Russian], Naukova Dumka, Kiev (1992).
Te-Jen Su and Chuan-Guey Huang, “Robust stability of delay dependence for linear uncertain systems,”IEEE Trans., Automat. Contr.,37, No. 10, 1656–1659 (1992).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 859–863, June, 1995.
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Khusainov, D.Y., Mustafaeva, R. Robust stability of systems with delay. Ukr Math J 47, 989–994 (1995). https://doi.org/10.1007/BF01058788
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DOI: https://doi.org/10.1007/BF01058788