TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Stability of nonlinear m-perturbed feedback controls systems

* , ,

* Corresponding author · click or hover a name for details

pp. 1685–1690Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1692XML
Published Online:
09 Dec 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1692
Pages:
1685–1690

Abstract

This paper examines the global and local stability of unstable nonlinear first- and second-order dynamical systems and the necessary conditions. More precisely, global and local stability is attained when these systems are controlled by m-perturbed feedback input controls functions. Finally, we obtain a dynamical system with m-perturbed feedback controls, a summation form with a nonlinear function that is exploited, and the stability of the systems supported by some illustrative examples.

Keywords

Subject Classifications

93C1031C45

References

[1] R. Al-Saphory, Z. Khalid and M. Jasim, Junction interface conditions for asymptotic gradient full-observer in Hilbert space, Italian Journal of Pure and Applied Mathematics, 49, p.p. 1-16 (2023).
[2] F. Glonaraghi   and B. Kuo, Automatic control systems, 9th ed., Wiley, USA. (2010).
[3] T. Tsay, Stability Analyses of Nonlinear Multivariable Feedback Control Systems, Wseas Transactions on Systems, 11.4, p.p. 140-151 (2012).
[4] S. AL-Azzawi and M. Aziz, Strategies of linear feedback control and its classification, Teklanika (Telecommunication Computing Electronics and Control), 17.4, p.p. 1931-1940 (2019).
[5] M. Aziz, S. Al-Azzawi, Control and synchronization with known and unknown parameters, Applied Mathematics, 7.3, p.p. 292-303 (2016).
[6] L. Chen, Y.  He, Y. Chai and R. Wu. New results on stability and stabilization of a class of nonlinear fractional-order systems, Nonlinear Dynamics, 75, 633-641 (2014). ‏
[7] M. De la Sen, About robust stability of Caputo linear fractional dynamic systems with time delays through fixed point theory. Fixed Point Theory and Algorithms for Sciences and Engineering, 2011.867932, p.p. 1-19, (2011). 
[8] R. Al-Saphory and A. El Jai, Regional asymptotic state reconstruction. International Journal of System Science, 33.13, p.p. 1025-1037 (2010).
[9] A. Pazy, Semigroup of Linear Operator and Applications to Partial Differential Equation. Springer-Verlag, New York, Inc (1983).
[10] H. Ye, J. Gao and Y. Ding, A generalized Gronwall inequality and its application to a fractional differential equation, Journal of Mathematical Analysis and Applications, 328(2), p.p. 1075-1081 (2007).  ‏
[11] R. Gorenflo, F. Mainardi and I. Podlubny, Fractional differential equations, Academic Press, Cambridge, 8, p.p. 683-699 (1999). ‏
[12] B. Yaghooti, K. Safavigerdini, R. Hajiloo, and H. Salarieh, Stabilizing unstable periodic orbit of unknown fractional-order systems via adaptive delayed feedback control, arXiv:228.06783, p.p. 1-9 (2023). ‏
[13] Shubham Sharma & Ahmed J. Obaid. Mathematical modelling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020), DOI: 10.1080/09720502.2020.1727611. 
[14] Abbood, Mohaimen M., Ebrahim, Hassan H., Al-Fayadh, Ali & Obaid, Ahmed J. () Measure defined on & Gamma; – algebra and some of their generalizations, Journal of Interdisciplinary Mathematics, 1-7, DOI: 10.47974/JIM-1502. 

Views: 136Downloads: 5Citations: 0