On reachability and controllability for a Volterra integro-dynamic system on time scales

Authors

  • Iguer Luis Domini DOS SANTOS Departamento de Matematica, Faculdade de Engenharia de Ilha Solteria, UNESP-Univ Estadual Paulista, Rua Rio de Janeiro, 266, Ilha Solteria, Sao Paulo CEP 15385-000, Brazil e-mail: iguer.santos@unesp.br https://orcid.org/0000-0001-5237-6024
  • Sanket TIKARE Department of Mathematics, Ramniranjan Jhunjhunwala College, Mumbai, Maharashtra 400 086, India e-mail: sankettikare@rjcollege.edu.in https://orcid.org/0000-0002-9000-3031

DOI:

https://doi.org/10.24193/subbmath.2025.1.08

Keywords:

Reachability, controllability, integro-dynamic equations, time scales

Abstract

The paper studies and relates the notions of reachability and controllability for the Volterra integro-dynamic system on time scales. More specifically, we obtain necessary and sufficient conditions for reachability and controllability. In addition, we obtain an equivalence between the concepts of reachability and controllability studied.

Mathematics Subject Classification (2010): 45D05, 34N05, 93B03, 93B05.

Received 01 March 2024; Accepted 20 March 2024.

References

[1] Adivar, M., Principal matrix solutions and variation of parameters for Volterra integro-dynamic equations on time scales, Glasg. Math. J., 53(2011), no. 3, 463-480.

[2] Adivar, M., Raffoul, Y.N., Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation, An. Științ. Univ. “Ovidius” Constanța Ser. Mat., 21(2013), no. 3, 17-32.

[3] Ben Nasser, B., Djemai, M., Defoort, M., Laleg-Kirati, T.-M., Time scale reachability and controllability of time-varying linear systems, Asian J. Control, 24(2022), no. 5, 2074-2088.

[4] Bohner, M., Peterson, A., Dynamic Equations on Time Scales, Birkhäuser Boston Inc., Boston, 2001.

[5] Brezis, H., Analyse Fonctionnelle : Théorie et Applications, Masson, Paris, 1983.

[6] Cabada, A., Vivero, D.R., Expression of the Lebesgue ∆-integral on time scales as a usual Lebesgue integral: Application to the calculus of ∆-antiderivatives, Math. Comput. Modelling, 43(2006), no. 1-2, 194-207.

[7] Guseinov, G.S., Integration on time scales, J. Math. Anal. Appl., 285(2003), no. 1, 107- 127.

[8] Karpuz, B., Koyuncuoğlu, H.C., Positivity and uniform exponential stability for Volterra integro-dynamical systems on time scales, Nonlinear Anal. Hybrid Syst., 41(2021), no. 3, Paper No. 101049, 15.

[9] Kumar, V., Malik, M., Controllability results for a Volterra integro-dynamic inclusion with impulsive condition on time scales, Rocky Mountain J. Math., 49(2019), no. 8, 2647-2668.

[10] Lupulescu, V., Ntouyas, S.K., Younus, A., Qualitative aspects of a Volterra integro-dynamic system on time scales, Electron. J. Qual. Theory Differ. Equ., 2013(2013), no. 5, 1-35.

[11] Younus, A., ur Rahman, G., Controllability, observability, and stability of a Volterra integro-dynamic system on time scales, J. Dyn. Control Syst., 20(2014), no. 3, 383-402.

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Published

2025-02-27

How to Cite

DOS SANTOS, I. L. D., & TIKARE, S. (2025). On reachability and controllability for a Volterra integro-dynamic system on time scales. Studia Universitatis Babeș-Bolyai Mathematica, 70(1), 115–126. https://doi.org/10.24193/subbmath.2025.1.08

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