References

• 1. 1)
     • 27. Prempain, E., Postlethwaite, I.: ‘Static output feedback stabilization with H∞ performance for a class of plants’, Syst. Control Lett., 2001, 43, (3), pp. 159–166.
  2. 2)
     • 2. Sabatier, J., Agrawal, O.P., Machado, J.A.T.: ‘Advances in fractional calculus: theoretical developments and applications in physics and engineering’ (2007, 50, pp. 613–615.
  3. 3)
     • 5. Oustaloup, A.: ‘La dérivation non entière: théorie, synthèse et applications’ (Hermes, Paris, 1995).
  4. 4)
     • 9. Sabatier, J., Moze, M., Farges, C.: ‘LMI stability conditions for fractional order systems’, Comput. Math. Appl., 2010, 9, (5), pp. 1594–1609.
  5. 5)
     • 13. Ibrir, S., Bettayeb, M.: ‘New sufficient conditions for observer-based control of fractional-order uncertain systems’, Automatica, 2015, 59, (9), pp. 216–223.
  6. 6)
     • 16. Farges, C., Peaucelle, D., Arzelier, D., et al: ‘Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs’, Syst. Control Lett., 2007, 56, (2), pp. 159–166.
  7. 7)
     • 1. Oustaloup, A.: ‘Diversity and non-integer differentiation for system dynamics’ (Wiley-ISTE, 2014).
  8. 8)
     • 17. Scherer, C., Gahinet, P., Chilali, M.: ‘Multiobjective output-feedback control via LMI optimization’, IEEE Trans. Autom. Control, 1997, 42, (7), pp. 896–911.
  9. 9)
     • 15. Ebihara, Y., Peaucelle, D., Arzelier, D.: ‘S-variable approach to LMI-based robust control’, Communications and control engineering' (Springer-Verlag, London, 2015).
  10. 10)
      • 26. Dong, J., Yang, G.H.: ‘Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties’, Automatica, 2013, 49, (6), pp. 1821–1829.
  11. 11)
      • 28. Crusius, C.A.R., Trofino, A.: ‘Sufficient LMI conditions for output feedback control problem’, IEEE Trans. Autom. Control, 1999, 44, (5), pp. 1053–1057.
  12. 12)
      • 21. Leite, V.J.S., Peres, P.L.D.: ‘An improved LMI condition for robust D-stability of uncertain polytopic systems’, IEEE Trans. Autom. Control, 2003, 48, (3), pp. 500–504.
  13. 13)
      • 14. Ibrir, S.: ‘On the dynamic-output feedback control of uncertain fractional-order linear systems’. Proc. European Control Conf., Aalborg, Denmark, 29 June–1 July 2016.
  14. 14)
      • 30. Samko, S.G., Kilbas, A.A., Marichev, O.I.: ‘Fractional integrals and derivatives: theory and applications’ (Gordon and Breach Science Publishers, 1987).
  15. 15)
      • 32. Lan, Y.H., Zhou, Y.: ‘LMI-based robust control of fractional-order uncertain linear systems’, Comput. Math. Applic., 2011, 62, (3), pp. 1460–1471.
  16. 16)
      • 24. Boyd, S., Ghaoui, L.E., Feron, E., et al: ‘Linear matrix inequality in systems and control theory’, ‘Studies in applied mathematics’ (SIAM, Philadelphia, 1994).
  17. 17)
      • 8. Trigeassou, J.C., Maamri, N., Sabatier, J., et al: ‘A Lyapunov approach to the stability of fractional-differential equations’, Analog Integr. Circuits Signal Process., 2011, 91, (3), pp. 437–445.
  18. 18)
      • 25. Boyd, S., Vandenberghe, L.: ‘Convex optimization’ (Cambridge University Press, 2004).
  19. 19)
      • 31. Annaby, M.H., Mansour, Z.S.: ‘q-fractional calculus and equations’, (Springer, Berlin, 2012), (Lecture Notes in Mathematics).
  20. 20)
      • 29. Ghaoui, L.E., Oustry, F., AitRami, M.: ‘A cone complementary linearization algorithm for static output feedback and related problems’, IEEE Trans. Autom. Control, 1997, 42, (8), pp. 1171–1176.
  21. 21)
      • 3. Manabe, S.: ‘The non-integer integral and its applications to control systems’, Jpn Inst. Electric. Eng., 1960, 80, pp. 589–597.
  22. 22)
      • 6. Matignon, D.: ‘Stability results on fractional differential equations with applications to control processing’, ‘Computational Engineering in Systems Applications’ (1996), Vol. 2, pp. 963–968.
  23. 23)
      • 11. Li, C., Wang, J., Lu, J., et al: ‘Observer-based stabilisation of a class of fractional order non-linear systems for 0<α<2 case’, IET Control Theory Applic., 2014, 8, (13), pp. 1238–1246.
  24. 24)
      • 19. Gutman, S., Jury, E.I.: ‘A general theory for matrix root-clustering in subregions of the complex plane’, IEEE Trans. Autom. Control, 1981, 26, (4), pp. 853–863.
  25. 25)
      • 12. Lan, Y.-H., Huang, H.-X., Zhou, Y.: ‘Observer-based robust control of a(1≤a<2) fractional-order uncertain systems: a linear matrix inequality approach’, IET Control Theory Applic., 2012, 6, (2), pp. 229–234.
  26. 26)
      • 22. Arzelier, D., Henrion, D., Peaucelle, D.: ‘Robust D-stabilization of a polytope of matrices’, Int. J. Control, 2002, 75, (10), pp. 744–752.
  27. 27)
      • 4. Oustaloup, A.: ‘Systèmes asservis linéaires d'ordre fractionaire: théorie et pratique’ (Masson, Paris, 1983).
  28. 28)
      • 23. Peaucelle, D., Arzelier, D., Bachelier, O., et al: ‘A new robust D-stability condition for real convex polytopic uncertainty’, Syst. Control Lett., 2000, 40, (1), pp. 21–30.
  29. 29)
      • 7. Farges, C., Moze, M., Sabatier, J.: ‘Pseudo-state feedback stabilization of commensurate fractional-order systems’, Automatica, 2010, 46, (10), pp. 1730–1734.
  30. 30)
      • 10. Ahn, H.S., Chen, Y.: ‘Necessary and sufficient stability condition of fractional-order interval linear systems’, Automatica, 2008, 44, (11), pp. 2985–2988.
  31. 31)
      • 20. Chilali, M., Gahinet, P., Apkarian, P.: ‘Robust pole placement in LMI regions’, IEEE Trans. Autom. Control, 1999, 44, (12), pp. 2257–2270.
  32. 32)
      • 18. de Oliveira, M.C., Bernussou, J., Geromel, J.C.: ‘A new discrete-time robust stability condition’, Syst. Control Lett., 1999, 37, (4), pp. 261–265.