Systems of linear differential equations with π-derivative and linear differential inclusions

Sbornik Mathematics

Volumn 196, Issue 11-12, 2005, Pages 1677-1691

  Plotnikova, N V ^a  

^a ODESSA NATIONAL UNIVERSITY   (Ukraine)

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EID: 33645133543     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2005v196n11ABEH003726     Document Type: Article

References (21)

1. A. I. Panasyuk and V. I. Panasyuk, Asymptotic optimization of nonlinear control systems, Izdat. Beloruss. Gos. Univ., Minsk 1977. (Russian)
2. A. A. Tolstonogov, Differential inclusions in a Banach space, Nauka, Novosibirsk 1986; English transl. Kluwer, Dordrecht 2000.
3. A. B. Kurzhanski and I. Valyi, "Ellipsoidal calculus for estimation and control", in Systems and control in the twenty first century (St. Louis, MO 1996), Birkhäuser, Boston 1997, pp. 229-243.
4. A. I. Ovseevich, "Extremal properties of ellipsoids approximating attainability sets", Problems Control Inform. Theory/Problemy Upravlen. Tear. Inform. 12:2 (1983), 1237-1240.
5. F. L. Chernous'ko, Estimation of the phase state of dynamical systems. The method of ellipsoids, Nauka, Moscow 1988. (Russian)
6. A. L. Dontchev, Perturbations, approximations and sensitivity analysis of optimal control systems, Springer-Verlag, Berlin 1983.
7. V. A. Plotnikov, A.V. Plotnikov, and F. N. Vityuk, Differential equations with multivalued right-hand side. Asymptotic methods, Astro-Print, Odessa 1999. (Russian)
8. M. S. Nikol'skiǐ, "A method of approximating an attainable set for a differential inclusion", Zh. Vychisl. Mat. Mat. Fiz. 28:8 (1988), 1252-1254;
9. English transl. in U.S.S.R. Comput. Math. Math. Phys. 28 (1988).
10. V. Veliov, "Second order discrete approximations to linear differential inclusions", SIAM J. Numer. Anal. 29 (1992), 439-451.
11. M. Hukuhara, "Integration des applications mesurables dont la valeur est un compact convexe", Funkcial Ekvac. 10 (1967), 205-223.
12. Yu. N. Tyurin, "Mathematical formulation of a simplified model of industrial planning", Ekonom. i Mat. Metody 1:3 (1965), 391-409. (Russian)
13. H. T. Banks and M.Q. Jacobs, "A differential calculus of multifunctions", J. Math. Anal. Appl. 29 (1970), 246-272.
14. H. Radström, "An embedding theorem for spaces of convex sets", Proc. Amer. Math. Soc. 3 (1952), 165-169.
15. E. S. Polovinkin, Theory of set-valued maps, Moscow Institute of Physics and Technology, Moscow 1983.
16. G. Debreu, "Integration of correspondences", Fifth Berkeley Sympos. Math. Statist, and Probability (Berkeley, Cal., 1965/66), Vol. II: Contributions to Probability Theory, Part 1, Univ. California Press, Berkeley 1967, pp. 351-372.
17. F. S. de Blasi and F. Iervolino, "Equazioni differential! con soluzioni a valore compatto convesso", Boll. Unione Mat. Ital. 2:4-5 (1969), 491-501.
18. R. J. Aumann, "Integrals of set-valued functions", J. Math. Anal. Appl. 12:1 (1965), 1-12.
19. V. I. Blagodatskikh and A. F. Filippov, "Differential inclusions and optimal control", Tr. Mat. Inst. Steklova 169 (1985), 194-252;
20. English transl. in Proc. Steklov Math. Inst. 169 (1985).
21. S. M. Markov, "Existence and uniqueness of solutions of the interval differential equation X' = F(t, X)", C. R. Acad. Sci. Bulgar. 31:12 (1978), 1519-1522.