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Existence of the kernel of a convex set in linear discrete control systems

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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

  1. J.-P. Aubin, “A Survey of viability theory,”SIAM J. Control Optim.,28, No. 4, 749–788 (1990).

    MATH  MathSciNet  Google Scholar 

  2. O. Hàjek, “Cores of targets in linear control systems,”Math. Systems Theory,8, No. 3, 203–206 (1974).

    MathSciNet  Google Scholar 

  3. 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).

    MathSciNet  Google Scholar 

  4. A. Z. Fazylov, “On the problem of evading collisions,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 3, 30–36 (1987).

    MathSciNet  Google Scholar 

  5. A. Z. Fazylov, “Existence of the kernel of a convex set in linear control systems,”Uzb. Mat. Zh., No. 1, 51–56 (1992).

    MathSciNet  Google Scholar 

  6. A. A. Chikrii, “Linear discrete quality games,”Kybernetika, No. 5, 90–99 (1971).

    MATH  Google Scholar 

  7. A. Azamov, “On the theory of pursuit-evasion discrete games, I,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 3, 3–8 (1978).

    MATH  Google Scholar 

  8. A. Azamov, “On the theory of pursuit-evasion discrete games, II,”Izv. Akad. Nauk Uzb. SSR, Ser. Fiz.-Mat., No. 6, 3–10 (1978).

    MATH  Google Scholar 

  9. A. Z. Fazylov, “Existence of the kernel of a set in control systems,”Dokl. Bolg. Akad. Nauk,42, No. 11, 37–38 (1989).

    MATH  MathSciNet  Google Scholar 

  10. R. Edwards,Functional Analysis, Holt, Rinehart, and Winston, New York (1965).

    Google Scholar 

  11. R. A. Horn and Ch. R. Johnson,Matrix Analysis, Cambridge University Press, London (1986).

    Google Scholar 

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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

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