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Preliminary Results

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Saturated Control of Linear Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 124))

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Abstract

In this chapter, all the needed material for the development in the sequel of this book is presented.

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References

  1. A. Baddou, H. Maarouf, A. Benzaouia, Partial eigenstructure assignment problem and its application to the constrained linear problem. Int. J. Sys. Sci. 44, 908–915 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Benzaouia, Application du concept d’invariance positive à l’étude des problèmes de commande des systèmes dynamiques discrets avec contraintes sur les entrées. Thesis of UPS LAAS, 88322, 1988

    Google Scholar 

  3. A. Benzaouia, C. Burgat, Regulator problem for linear discrete-time systems with non-symmetrical constrained control. Int. J. Control. 48(6), 2441–2451 (1988)

    Article  MATH  Google Scholar 

  4. A. Benzaouia, C. Burgat, Existence of non symmetrical Lyapunov functions for linear systems. Int. J. Syst. Sc. 20, 560–597 (1989)

    MATH  Google Scholar 

  5. A. Benzaouia, A. Hmamed, Regulator problem for linear continuous-time systems with non-symmetrical constrained control. IEEE Trans. Aut. Control. 38(10), 1556–1560 (1993)

    Article  MATH  Google Scholar 

  6. A. Benzaouia, Resolution of equation XA+XBX=HX and the pole assignment problem. IEEE Trans. Aut. Control. 40(10), 2091–2095 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Benzaouia, Saturated switching systems. LNC 426 (Springer, 2012). ISBN-13: 978-1447128991

    Google Scholar 

  8. A. Benzaouia, M. Darouach, A. Hmamed, Solution of equation XA + XBXE = HXE and the pole assignment for singular systems. IMA J. Math. Control. Inf. 29(3), 343–356 (2012)

    Article  MATH  Google Scholar 

  9. F. Blanchini, Feedback control for linear systems with state and control bounds in the presence of disturbance. IEEE Trans. Aut. Control. 35, 1131–1135 (1990)

    Article  MathSciNet  Google Scholar 

  10. F. Blanchini, Feedback control for linear time invariant systems with states and control bounds in the presence of disturbances. IEEE Trans. Aut. Control. 35, 1234 (1992)

    MathSciNet  MATH  Google Scholar 

  11. F. Blanchini, Set Invariance in control. Automatica 35, 1747–1767 (1999)

    MathSciNet  Google Scholar 

  12. Y. Y. Cao, Z. Lin, Stability analysis of discrete-time systems with actuator saturation by saturation dependent Lyapunov function in Proceedings of the 41th IEEE CDC, Las Vegas, USA, (2002)

    Google Scholar 

  13. E.B. Chegancas, S. Tarbouriech, On positive invariance and output feedback stabilization of input constrained linear systems in Proceeding of the ACC, Baltimore, U.S.A., (1994), pp. 2740–2744,

    Google Scholar 

  14. L. Dai, Lecture Notes in Control and Information Sciences, in Singular Control Systems (Springer, Berlin, 1989)

    Google Scholar 

  15. P.O. Gutman, P. Hagander, A new design of constrained controllers for linear systems. IEEE Trans. Aut. Control. 30, 22–33 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Haar, Über lineare Ungleichungen. 1918, Reprinted in: Alfred Haar, Gesammelte Arbienten (Akadémai Kiadó, Bubapest 1959)

    Google Scholar 

  17. J.C. Hennet, Une extension du lemme de Farkas et son application au problème de régulation linéaire sous constraintes. Comptes-rendus de l’Académie des Sciences, 308, Série I, 415–419 (1989)

    Google Scholar 

  18. T. Hu, Z. Lin, The equivalence of several set invariance conditions under saturation in Proceeding of the 41th IEEE CDC (Las Vegas, USA, 2002)

    Google Scholar 

  19. T. Hu, Z. Lin, B.M. Chen, Analysis and design for discrete-time linear systems subject to actuator saturation. Syst. Control. Lett. 45, 97–112 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Kaustky, N.K. Nichols, E.K.W. Chu, Robust pole assignment in singular systems. Linear Algebr. Appl. 121, 9–37 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  21. H. Maarouf, The resolution of the equation XA+XBX=HX and the pole assignment problem: a general approach. Automatica 79, 162–66 (2017)

    Article  MathSciNet  Google Scholar 

  22. J. R. Magnus, H. Neudecker, Matrix differential calculus with application in statistic and econometrics, (Wiley, 1988)

    Google Scholar 

  23. F. Mesquine, D. Mehdi, Constrained observer based controller for linear continuous time systems. Int. J. Syst. Sci. 27(12), 1363–1369 (1996)

    Article  MATH  Google Scholar 

  24. F. Mesquine, F. Tadeo, A. Benzaouia, Regulator problem for linear systems with constrained control and its increment in Proceedings of the 15th IFAC, Barcelona, Spain, (2002)

    Google Scholar 

  25. F. Mesquine, A. Benlemkadem, Robust linear constrained regulator problem. IMA J. Math. Control. Inf. (2006). doi:10.1093/imamci/dn1015

    MATH  Google Scholar 

  26. B.E.A. Milani, A.N. Carvalho, Robust linear regulator design for discrete-time systems under polyhedral constraints. Automatica 31, 1489–1493 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  27. A.A. Ten Dam, J.W. Nieuwenhuis, A linear programming algorithm for invariant polyhedral sets of discrete-time linear systems. Syst. Control. Lett. 25, 337–341 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  28. M. Vassilaki, G. Bitsoris, Constrained regulation of linear continuous-time dynamical systems. Syst. Control. Lett. 13, 247–252 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  29. M. Vassilaki, J.C. Hennet, G. Bitsoris, Feedback control of linear discrete-time system under state and control constraints. Int. J. Control. 47, 1727–1735 (1988)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Abdellah Benzaouia .

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Benzaouia, A., Mesquine, F., Benhayoun, M. (2018). Preliminary Results. In: Saturated Control of Linear Systems. Studies in Systems, Decision and Control, vol 124. Springer, Cham. https://doi.org/10.1007/978-3-319-65990-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-65990-9_1

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