Domination and minimum energy problem in linear time-varying systems
DOI:
https://doi.org/10.5269/bspm.82895Resumo
This paper investigates the notion of domination in time-varying linear perturbed systems. The primary objective of this work is to study the comparison (or classification) of input operators, with respecting the output one. We present the characterization and property results of this concept. We study the optimal control which ensures the domination of time-varying disturbed systems.
Referências
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8. Huang, Y., and Xue, W., Active disturbance rejection control: Methodology and theoretical analysis, ISA transactions,
53:4, 963?976, (2014).
9. Larrache A., Lhous M., Ben Rhila S., Rachik M., Tridane A., An output sensitivity problem for a class of linear
distributed systems with uncertain initial state. Archives of Control Sciences, 30(1): 77-93, (2020).
10. Magri E.M., Amissi C., Afifi L., Lhous M., On the minimum energy compensation for linear time-varying disturbed
systems. Archives of Control Sciences, Volume 32(LXVIII), No. 4, pages 1-22, 2022. 10.24425/acs.2022.143669, (2022).
11. Mei, Q., She, J., Liu, Z. et al. Estimation and compensation of periodic disturbance using internal-model-based
equivalent-input-disturbance approach. Sci. China Inf. Sci. 65, 182205, https://doi.org/10.1007/s11432-020-3192-5,
(2022).
12. Rachik M., Lhous M., An Observer-based control of linear systems with uncertain parameters, Archives of Control
Sciences, Volume 26(LXII), No. 4, pp. 565-576, (2016).
13. Souhail S., and Afifi L., Cheap controls for disturbances compensation in hyperbolic delayed systems. International
Journal of Dynamical Systems and Differential Equations, 10:6, 511-536, (2020).
14. Yu, P., Wu, M., She, J.H., Robust tracking and disturbance rejection for linear uncertain system with unknown state
delay and disturbance. IEEE/ASME Trans Mechatron, 23: 1445-1455, (2018).
6(19):913-924, (2012).
2. Amissi C., Magri E. M., Lhous M., and Afifi L., Compensation Problem in Linear Fractional Order Disturbed Systems.
Mathematical Modelling and Analysis. Volume 29, Issue 3, 546-559, 2024. https://doi.org/10.3846/mma.2024.18927,
(2024).
3. Amissi C., Magri E. M., Lhous M., and Afifi L., Remediability problem in linear time-varying systems with disturbances.
Bol. Soc. Paran. Mat. v. 2025 (43) : 1-19. ISSN-0037-8712. https://doi:10.5269/bspm.76256, (2025).
4. Chang A., An algebraic characterization of controllability. IEEE Trans. Automatic Control, AC-10, pp. 112-113, (1965).
5. Curtain R.F., Pritchard A.J., Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information
Sciences, vol. 8, Berlin, (1978).
6. Fenga, H. , Wu, X.H., and Guo, B.Z., Dynamics Compensation in Observation of Abstract Linear Systems.
arXiv:2009.01643. https://doi.org/10.48550/arXiv.2009.01643. 3 Sep (2020).
7. Hizazi H., Amissi C., Lhous M., Magri E. M., Domination in linear fractional-order distributed systems. MATHEMATICAL MODELING AND COMPUTING, Vol. 11, No. 2, pp. 455-462, (2024).
8. Huang, Y., and Xue, W., Active disturbance rejection control: Methodology and theoretical analysis, ISA transactions,
53:4, 963?976, (2014).
9. Larrache A., Lhous M., Ben Rhila S., Rachik M., Tridane A., An output sensitivity problem for a class of linear
distributed systems with uncertain initial state. Archives of Control Sciences, 30(1): 77-93, (2020).
10. Magri E.M., Amissi C., Afifi L., Lhous M., On the minimum energy compensation for linear time-varying disturbed
systems. Archives of Control Sciences, Volume 32(LXVIII), No. 4, pages 1-22, 2022. 10.24425/acs.2022.143669, (2022).
11. Mei, Q., She, J., Liu, Z. et al. Estimation and compensation of periodic disturbance using internal-model-based
equivalent-input-disturbance approach. Sci. China Inf. Sci. 65, 182205, https://doi.org/10.1007/s11432-020-3192-5,
(2022).
12. Rachik M., Lhous M., An Observer-based control of linear systems with uncertain parameters, Archives of Control
Sciences, Volume 26(LXII), No. 4, pp. 565-576, (2016).
13. Souhail S., and Afifi L., Cheap controls for disturbances compensation in hyperbolic delayed systems. International
Journal of Dynamical Systems and Differential Equations, 10:6, 511-536, (2020).
14. Yu, P., Wu, M., She, J.H., Robust tracking and disturbance rejection for linear uncertain system with unknown state
delay and disturbance. IEEE/ASME Trans Mechatron, 23: 1445-1455, (2018).
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Publicado
2026-07-01
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Conf. Issue: Recent Advances in Applied Mathematics, Modeling, and Engineering
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Copyright (c) 2026 Boletim da Sociedade Paranaense de Matemática
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
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Como Citar
Amissi, C., Magri, E. M., Magri, E. M., & Lhous, M. (2026). Domination and minimum energy problem in linear time-varying systems. Boletim Da Sociedade Paranaense De Matemática, 44(18), 1-11. https://doi.org/10.5269/bspm.82895
