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Null-Controllability of Linear Systems on Time Scales

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Języki publikacji
EN
Abstrakty
EN
The purpose of the paper is to study the problem of controllability of linear control systems with control constrains, defined on a time scale. The obtained results extend the existing ones on any time domain. The set of values of admissible controls is a given closed and convex cone with nonempty interior and vertex at zero or is a subset of containing zero.
Rocznik
Strony
50--55
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
Bibliografia
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  • 2. Agrawal R.P., Otero-Espinar V., Perera K., Vivero D. (2006), Basic properties of Sobolev’s spaces on time scales, Advances in Difference Equations, article ID 38121, 1-14.
  • 3. Ahmed N.U (1985), Finite-time null controllability for a class of linear evolution equations on a Banach space with control constraints, Journal of Optimization Theory and Applications, 47(2), 129-158.
  • 4. Bartosiewicz Z., Piotrowska E., Wyrwas M. (2007), Stability, stabilization and observers of linear control systems on time scales, Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 2803-2808.
  • 5. Bartosiewicz Z., Pawluszewicz E. (2006), Realizations of linear control systems on time scales, Control & Cybern, 35(4), 769–786.
  • 6. Bartosiewicz Z., Pawluszewicz E. (2008), Realizations of nonlinear control systems on time scales, IEEE Transactions on Automatic Control , 53(2), 571-575.
  • 7. Benzaid Z., Lutz D.A. (1988), Constrained controllability of perturbed discrete-time systems, Int. J. Control, 48(2), 655-673.
  • 8. Bohner M., Petrson A. (2001), Dynamic equations on time scales, Birkhäuser.
  • 9. Bohner M., Petrson A. (2003), Advances in dynamic equations on time scales, Birkhäuser.
  • 10. Cabada A, Vivero D.R. (2005), Criterions for absolute continuity on times cales, Journal of Difference Equations and Applications, Vol. 11(11), 1013–1028.
  • 11. Cabada A., Vivero, D.R. (2006), Expression of the Lebesgue -integral on time scales as a usual Lebesgue integral: application to the calculus of ∆-antiderivatives. Math. Comput. Model, 43(1–2), 194–207.
  • 12. Chukwu E.N., Lenhart S.M. (1991), Controllability questions for nonlinear systems in abstract spaces, Journal of Optimization Theory and Applications, 68(3), 432-462.
  • 13. DaCunha J.J., Davis J.M. (2011), A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems, Journal of Difference Equations, 251, 2987-3027.
  • 14. Davis J.M., Gravagne I.A., Jackson B.J., Marks II R.J. (2009), Controllability, observability, realizability, and stability of dynamic linear systems, Electronic Journal of Differential Equation, No. 37, 1-32.
  • 15. Deniz A. (2009), Measure theory on time scales. MSc thesis, Graduate School of Engineering and Sciences of Izmir Institute of Technology, Turkey.
  • 16. Ferreira R.A.C., Torres D.F.M. (2010), Isoperimetric Problems of the Calculus of Variations on Time Scales, Nonlinear Analysis and Optimization Ii: Optimization, 514, 123-131 .
  • 17. Gravagne I.A., Davis J.M., DaCunha J.J. (2009), A unified approach to high-gain adaptive controllers, Abstract and Applied Analysis, 2009, 1-13.
  • 18. Jackson B.J. (2007), A General Linear Systems Theory on Time Scales: Transforms, Stability, and Control, PhD Thesis, Baylor University.
  • 19. Klamka J. (1991), Controllability dynamic systems, Kluwer.
  • 20. Mozyrska D., Pawłuszewicz E. (2008), Functional series on time scales, International Journal of Mathematics and Statisctics, 2(S08), 95 -106
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  • 22. Path V.N., Park J.Y., Jung I.H. (2000), Stability and constrained controllability of linear systems in Banach spaces, J.Korean Math. Soc., 37(4), 593-611.
  • 23. Pawłuszewicz E., Torres D.F.M. (2010), Avoidance control on time scales, J. Optim. Theory Appl., 145, 527-542.
  • 24. Pötzsche P., Siegmund S., Wirth F. (2003), A spectral characterization of expnential stability for linear time-invariant systems on time scales. Discrete and Continuous Dynamical Systems 9(5), 1223 - 1241.
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  • 26. Sontag E. (1998), Mathematical Control Theory, Springer – Verlag.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0074-0004
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