Abstract
Necessary and sufficient conditions for the existence of the kernel of a convex set in linear discrete control systems are obtained.
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References
J.-P. Aubin, “A Survey of viability theory,”SIAM J. Control Optim.,28, No. 4, 749–788 (1990).
O. Hàjek, “Cores of targets in linear control systems,”Math. Systems Theory,8, No. 3, 203–206 (1974).
A. B. Kurzhanskii and T. F. Filippova, “Description of a beam of surviving trajectories in a control system,”Differentsial'nye Uravneniya [Differential Equations],23, No. 8, 1303–1315 (1987).
A. Z. Fazylov, “On the problem of evading collisions,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 3, 30–36 (1987).
A. Z. Fazylov, “Existence of the kernel of a convex set in linear control systems,”Uzb. Mat. Zh., No. 1, 51–56 (1992).
A. A. Chikrii, “Linear discrete quality games,”Kybernetika, No. 5, 90–99 (1971).
A. Azamov, “On the theory of pursuit-evasion discrete games, I,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 3, 3–8 (1978).
A. Azamov, “On the theory of pursuit-evasion discrete games, II,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 6, 3–10 (1978).
A. Z. Fazylov, “Existence of the kernel of a set in control systems,”Dokl. Bolg. Akad. Nauk,42, No. 11, 37–38 (1989).
R. Edwards,Functional Analysis, Holt, Rinehart, and Winston, New York (1965).
R. A. Horn and Ch. R. Johnson,Matrix Analysis, Cambridge University Press, London (1986).
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Translated fromMatematicheskie Zametki, Vol. 58, No. 1, pp. 119–126, July, 1995.
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Fazylov, A.Z. Existence of the kernel of a convex set in linear discrete control systems. Math Notes 58, 757–761 (1995). https://doi.org/10.1007/BF02306185
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DOI: https://doi.org/10.1007/BF02306185