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Weak asymptotic stability at first approximation for periodic differential inclusions

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Abstract

Weak asymptotic stability of an equilibrium position for a periodic differential inclusion is studied. First the weak asymptotic stability for a discrete-time inclusion generated by the original differential inclusion is investigated with the help of first approximation techniques. Then using the results for discrete-time inclusions the weak asymptotic stability for the differential inclusion is derived from the properties of its first approximation.

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References

  1. J.-P. AUBIN, Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions, inAdvances in Math. Suppl. Studies, pages 160–232, Acad. Press, New York, 1981

    Google Scholar 

  2. J.-P. AUBIN, A. CELLINA,Differential Inclusions, Springer-Verlag, New York, 1984

    Google Scholar 

  3. J.-P. AUBIN, H. FRANKOWSKA, C. OLECH, Controllability of convex processes,SIAM J. Control 24, 1192–1211 (1986)

    Google Scholar 

  4. A. F. FILIPPOV,Differential Equations with Discontinuous Right-Hand Sides, Kluwer Acad. Publishers, 1988.

  5. H. FRANKOWSKA, Contrôlabilité locale et propriétés des semi-groupes de correspondances,C.R.A.S. 299, Sér. 1, 165–168 (1983)

    Google Scholar 

  6. H. FRANKOWSKA, The maximum principle for a differential inclusion problem, inLect. Notes Contr. Inf. Sci. 62, 517–531 (1984)

  7. V. I. KOROBOV, A. P. MARINIC, E. N. PODOLSKII, Controllability of linear autonomous systems in the presence of constraints on the control,Diff. Equat. 11, 1465–1475 (1975)

    Google Scholar 

  8. V. I. KOROBOV, NGUEN KHOA SHON, σ-controllability of linear autonomous systems in the presence of constraints on the control,Diff. Equat. 16, 242–248 (1980)

    Google Scholar 

  9. M. A. KRASNOSELSKI,Translation Along Trajectories of Differential Equations, AMS, Providence, 1968

    Google Scholar 

  10. P. KRBEC, Weak stability of multivalued differential equations,Czechosl. Math. Journ. 26, 470–476 (1976)

    Google Scholar 

  11. A. M. LYAPUNOV,Problème Général de la Stabilité du Mouvement, Annals of Mathematics Studies, no. 17, Princeton Univ. Press, Princeton, N. J. Oxford Univ. Press, London 1947

    Google Scholar 

  12. E. S. POLOVINKIN, G. V. SMIRNOV, An approach to differentiation of setvalued maps and necessary conditions of optimality for differential inclusions,Diff. Equat. 22, 660–668 (1986)

    Google Scholar 

  13. E. S. POLOVINKIN, G. V. SMIRNOV, Time-optimal problem for differential inclusions,Diff. Equat. 22, 940–952 (1986)

    Google Scholar 

  14. R. T. ROCKAFELLAR,Convex Analysis, Princeton Univ. Press, 1970

  15. E. ROXIN, Stability in general control systems,J. Diff. uat.1, 115–150 (1965)

    Google Scholar 

  16. G. V. SMIRNOV, Weak asymptotic stability for differential inclusions, I,Automat. Remote Control 5, n. 7, part 1, 901–9081 (1990)

    Google Scholar 

  17. G. V. SMIRNOV, Weak asymototic stability for differential inclusions, II,Automat. Remote Control. 51, n.8, part 1, 1052–1058 (1990)

    Google Scholar 

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  1. International School for Advanced Studies, via Beirut n. 2-4, 34013, Trieste, Italy

    Georgi V. Smirnov

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  1. Georgi V. Smirnov
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Smirnov, G.V. Weak asymptotic stability at first approximation for periodic differential inclusions. NoDEA 2, 445–461 (1995). https://doi.org/10.1007/BF01210619

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  • DOI: https://doi.org/10.1007/BF01210619

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