Stabilizability of non-linear dynamic control systems on time scales in Banach spaces

Laabi, Nada A.; Al-Sabti, Ansam

doi:10.47974/JIM-2083

Open Access Research Article

Stabilizability of non-linear dynamic control systems on time scales in Banach spaces

^*Nada A. LaabiCorresponding authornadahuseen@utq.edu.iqDepartment of Mathematics College of Computer Science and Mathematics University of Thi-QarThi-Qar, IraqView full profile → , Ansam Al-Sabtiansam.abdulrahman@uobasrah.edu.iqDepartment of Mathematics Faculty of Education for Pure Sciences University of BasrahBasrah, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 1073–1079Vol. 28Issue 3-BApril 2025DOI: 10.47974/JIM-2083XML

Received:: 15 Oct 2024
Published Online:: 08 May 2025
Article type:: Research Article
Language:: EN
Article no.:: JIM-2083
Pages:: 1073–1079

Abstract

In this article, new method is proposed to study the stabilizability of a nonlinear dynamic control systems ȶΔ (ϰ)=A(ϰ)ȶ(ϰ)+B(ϰ)u(ϰ)+g(ϰ,ȶ(ϰ),u(ϰ)), ϰ∈T on a time scale T. Based on using an appropriate Lyapunov function and the derivation of sufficint conditions to be this system, uniformly stabilizable and h – stabilizable. Here, A, B ∈ L(X). Further, different numerical examples were given as an application.

Keywords

Time scales Dynamical control system Uniformly stabilizable h – stabilizable

Subject Classifications

46N1047N1090C30

References

[1] Z. Bartosiewicz and E. Pawuszewicz, Realizations of linear control systems on time scales, Control & Cybernetics, vol. 35, no. 4, pp.769–786 (2006).
[2] M. Bohner and Allan Peterson, Dynamic equations on time scales, An introduction with Applications, Birkhäuser, Boston Inc., Boston, MA (2001).
[3] M. Bohner and Allan Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser Boston, Massachusetts (2003).
[4] S. Boyd, L. El Ghaoui, Eric Feron, and V. Balakrishnan, Linear Matrix Inequalities in System And Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA (1994).
[5] S. K. Choi, N. J. Koo, and D. M. Im, h-stability for linear dynamic equations on time scales, Journal of Mathematical Analysis and Applications, vol. 324, no. 1, pp.707–720 (2006).
[6] J. J. Da. Cunha, Stability for time varying linear dynamic systems on time scales, Journal of Computational and Applied Mathematics, vol. 176, no. 2, pp.381–410 (2005).
[7] S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. no. 18, pp.18-56 (1990).
[8] K. U. Kristiansen, A Review of Multiple-Time-Scale Dynamics: Fundamental Phenomena and Mathematical Methods, In Mathematics Online First Collections (pp. 1-55). Springer. (2023).
[9] Nada A. Laabi and Azhar A. Sangoor, “A study of stability for nonlinear differential equations in Banach spaces on time scales,” International Journal of Innovative Science Engineering and Technology, Vol. 11, Issue 01, January (2024).
[10] M. M. Abbood, H. H. Ebrahim, A. Al-Fayadh, and A. J. Obaid, “Measure defined on Γ-algebra and some of their generalizations,” Journal of Interdisciplinary Mathematics, vol. 26, no. 5, pp. 821–827 (2023), doi: 10.47974/JIM-1502.
[11] I. S. Ahmed, H. H. Ebrahim, and A. Al-Fayadh, “γ– algebra of Sets and Some of its Properties,” Iraqi J. Sci., vol. 63, no. 11, pp. 4918–4927 (2022), doi: 10.24996/ijs.2022.63.11.28.
[12] A. S. Mohammed, S. H. Asaad, and I. S. Ahmed, “New properties of strongly regular left almost semi-group,” J. Discret. Math. Sci. Cryptogr., vol. 25, no. 2, pp. 615–622 (2022), doi: 10.1080/09720529.2021.1982491.

Views: 98Downloads: 4Citations: 0