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An Output Sensitivity Problem for a Class of Fractional Order Discrete-Time Linear Systems


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1. Abdelhak A., M. Rachik M. (2019), Model reduction problem of linear discrete systems: Admissibles initial states, Archives of Control Sciences, volume 29(LXV), no. 1, pages 41-55, 2019. Search in Google Scholar

2. Abdelilah LarracheL., Mustapha LhousL., Soukaina Ben B.RhilaR., Mostafa Rachik R. Abdessamad TridaneT. (2020), An output sensitivity problem for a class of linear distributed systems with uncertain initial state, Archives of Control Sciences, volume 30(LXVI), no. 1, pages 139-155, 2020. Search in Google Scholar

3. Amine El Bhih.B., Youssef BenfatahB., Mostafa RachikR. (2020), Exact determination of maximal output admissible set for a class of semilinear discrete systems, Archives of Control Sciences, ACS volume 30(LXVI), no. 3, pages 523-552, 10.24425/acs.2020.134676, 2020. Search in Google Scholar

4. Andrzej Dzielinski A., and Dominik Sierociuk D. (2008), Stability of Discrete Fractional Order State-space Systems. Journal of Vibration and Control, 14: 1543, 2008. Search in Google Scholar

5. Arild Thomson A. (2007), International journal of systems science, Identifiability of dynamic systems, volume 9, pages 813-825, Issue 2007.10.1080/00207727808941738 Search in Google Scholar

6. Balatif, O., Rachik, M., Labriji, E. houssine, Rachik, Z. (2016).), Optimal control problem for a class of bilinear systems via block pulse functions. IMA Journal of Mathematical Control and Information, dnw005. doi:10.1093/imamci/dnw005.10.1093/imamci/dnw005 Search in Google Scholar

7. Buslowicz M. (1983), On some properties of the solution of state equation of discrete-time systems with delays, Zesz.Nauk. Polit. Bial., Elektrotechnika, vol. 1, pp. 17-29, 1983 in Polish. Search in Google Scholar

8. Chi-Tsong ehenE. (2008), Analog and Digital control system design transfer-function, state space, Algebraic Methods. State University of New York at Stony Broak, Springer 2008. Search in Google Scholar

9. Chraïbi, L., Karrakchou, J., Rachik, M., Ouansafi, A. (2006),. Linear quadratic control problem with a terminal convex constraint for discrete-time distributed systems. IMA Journal of Mathematical Control and Information, 23(3), 347-370. doi:10.1093/imamci/dni063.10.1093/imamci/dni063 Search in Google Scholar

10. D.W.Gu D.W., P.Hr.Petkov P.Hr. and, M.M.Konstantinov M.M. (2005), Robust control design with Matlab, Springer 2005.. Search in Google Scholar

11. Debnath L. (2003.), Recent Applications of Fractional Calculus to Science and Engineering. IJMMS, Hindawi Publishing, volume 54, pp. 3413-3442, 2003. Search in Google Scholar

12. Dórea, C. E. T., and Hennet, J. C. (1996), Computation of Maximal Admissible Sets of Constrained Linear Systems, Proceedings of the 4th IEEE Mediterranean Symposium on New Directions on Control and Automation, Maleme, Greece, pp. 286291, 1996. Search in Google Scholar

13. Dzieliński and A.D., Sierociuk D. (2005), Adaptive Feedback Control of Fractional Order Discrete-Time State-Space Systems. Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation, and International Conference on Intelligent Agents, Web Technologies and Internet Commerce, CIMCA-IAWTIC’05, 2005. Search in Google Scholar

14. Ferreira, R.A.C., and Torres, D.F.M. (2011), Fractional h-Difference Equations Arising from the Calculus of Variations, Applicable Analysis and Discrete Mathematics, 5, 110-121, 2011.10.2298/AADM110131002F Search in Google Scholar

15. Franklin (2001), Feedback control of dynamic systems, 5th edition, springer 2001. Search in Google Scholar

16. Gilbert E. G. and, Tan K. T. (1991), Linear systems with state and control constraints: the theory and application of maximal output admissible sets, in IEEE Transactions on Automatic Control, vol. 36, no. 9, pp. 1008-1020, Sept 1991. Search in Google Scholar

17. Haim BrezisB., Functional Analysis, Sobolev Spaces and Partial Differential Equations, ISBN 978-0-387-70913-0, doi:10.1007/978-0-387-70914-7.10.1007/978-0-387-70914-7 Search in Google Scholar

18. Hilfer, R., ed. (2000), Application of Fractional Calculus in Physics, World Scientific, Singapore, 2000.10.1142/3779 Search in Google Scholar

19. J.L.Lions J.L. (1988,), Sur les sentinelles des systèmes distribués.C.R.A.S. Paris, t. 307. Le cas des conditions initiales incomplètes, p. 819-893. Conditions frontières, termes sources. coefficients incomplètement connus, p.865-870, 1988.. Search in Google Scholar

20. Joycer OsorioO., Hamid R. OssarehO. (2018), A Stochastic Approach to Maximal Output Admissible Sets and Reference Governors, Control Technology and Applications (CCTA) 2018 IEEE Conference on, pp. 704-709, 2018. Search in Google Scholar

21. Kaczorek, T. (2007), Reachability and Controllability to Zero of Cone Fractional Discrete-time Systems, Archives of Control Sciences, 17, 357-367, 2007.10.23919/ECC.2007.7068247 Search in Google Scholar

22. Kaczorek, T. (2008), Reachability of Fractional Positive Continuous-time Linear Systems, International Journal of Applied Mathematics and Computer Science, 18, 223-228, 2008.10.2478/v10006-008-0020-0 Search in Google Scholar

23. Kauffmann. M, Bretthawer. G., Identifiability of the linear closed loop systems, Control Systems, Robotics and Automation, volume V, pages 127-138. Search in Google Scholar

24. Kilbas A. A., Srivastava H. M. and, Trujillo. J. J. (2006), Theory and Application of Fractional Differential Equations North Holland Mathematics Studies, Editor Jan van Mill, Elsevier, 2006. Search in Google Scholar

25. Kolmanovsky I., Gilbert E.G. (1998), Theory and computation of disturbance invariance sets for discrete-time linear systems, Mathematical Problems in Engineering: Theory, Methods and Applications, vol. 4, pp. 317-367, 1998. Search in Google Scholar

26. Lions J.L. (1992), Sentinelles pour les systèmes distribués à données incomplètes, Recherches en Mathematiques Appliquées 21, Masson, Paris, 1992. Search in Google Scholar

27. Lions, J.L. (1988), Sentinels for periodic distributed systems. Chinese Annals of Math B. Vol. 10. p 213-225. Search in Google Scholar

28. Namerikawa T., W. Shinozuka W., and M., Fujita M. (2004), : Disturbance and Initial State Uncertainty Attenuation Control for Magnetic Bearings, In Proceedings 9th International Symposium on Magnetic Bearings, pp. 3-6, 2004.. Search in Google Scholar

29. Ogata Katsuhiko O. (1995), Discrete time control systems, Prentice Hall internatiounal editions 1995. Search in Google Scholar

30. Oldham K. B. and ., J. Spanier J. (1974),. The Fractional Calculus. Academic Press, 1974. Search in Google Scholar

31. Podlubny I. (1999), Fractional Differential Equations. Academic Press, 1999. Search in Google Scholar

32. Rachik M., M. Lhous M., A. Tridane A. (2002), On the Maximal Output Admissible Set for a Class of Nonlinear Discrete Systems, Systems Analysis Modelling Simulation, 42:11, 1639-1658, DOI: 10.1080/716067174.10.1080/716067174 Search in Google Scholar

33. Rachik, M., Lhous, M. (2016), An observer-based control of linear systems with uncertain parameters. Archives of Control Sciences, 26(4), 565-576. doi:10.1515/acsc-2016-0031, 2016.10.1515/acsc-2016-0031 Search in Google Scholar

34. Robert L.Payne R.L., Graham C.GoodwinG. (2007), International journal of control, On the identifiability of linear systems, volume 20, Issues 5, 2007, pages 865-868.10.1080/00207177408932788 Search in Google Scholar

35. Rosario ToscanoT. (2005), Commande et diagnostic des systèmes dynamiques, Ellipses 2005.. Search in Google Scholar

36. Sawadogo S. (2020), Control of a migration problem of a population by the sentinel method, Journal of Nonlinear Evolution Equations and Applications, Volume 2020, Number 3, pp. 37-53, March 2020.. Search in Google Scholar

37. Sierociuk, D., and Dzieliński, A. (2006,), Fractional Kalman Filter Algorithm for the States, Parameters and Order of Fractional System Estimation, International Journal of Applied Mathematics and Computer Science, 16, 129-140, 2006. Search in Google Scholar

38. Yamamoto K. (2019), Time-variant feedback controller based on capture point and maximal output admissible set of a humanoid, Advanced Robotics, 33:18, 944-955, 2019.10.1080/01691864.2019.1633403 Search in Google Scholar