Pseudo-state feedback stabilization of commensurate fractional order systems

Automatica

Volumn 46, Issue 10, 2010, Pages 1730-1734

  Farges, Christophe ^a   Moze, Mathieu ^a   Sabatier, Jocelyn ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Commensurate fractional order systems; Linear matrix inequalities; Polytopic systems; State feedback

Indexed keywords

BELONG TO; COMPLEX PLANES; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LINEAR MATRIX; LMI-CONDITION; POLYTOPIC SYSTEM; STABILITY CONDITION; STABILITY REGIONS; STABILIZING CONTROLLERS; STATE MATRICES; STATE-FEEDBACK STABILIZATION;

ALGEBRA; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK; FREQUENCY SELECTIVE FADING; LINEAR MATRIX INEQUALITIES; ROBUST CONTROL; STABILIZATION; SWITCHING SYSTEMS;

STATE FEEDBACK;

EID: 77956400175     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2010.06.038     Document Type: Article

References (17)

1. P. Apkarian, P. Gahinet, and G. Becker Self-scheduled H∞ control of linear parameter-varying systems: a design example Automatica 31 9 1995 1251 1261
2. Bachelier, O. (1998). Commande des systèmes linéaires incertains: placement de pôles robuste en D-stabilité. Ph.D. thesis. Institut National des Sciences Appliques.
3. O. Bachelier, and B. Pradin Bounds for uncertain matrix root-clustering in a union of subregions International Journal of Robust and Nonlinear Control 9 1999 333 359
4. J. Bernussou, J.C. Geromel, and P.L.D. Peres A linear programming oriented procedure for quadratic stabilization of uncertain systems Systems & Control Letters 13 1 1989 65 72
5. S. Boyd, and L. Vandenberghe Convex optimization 2004 Cambridge University Press
6. M. Caputo Linear models of dissipation whose q is almost frequency independentII Geophysical Journal International 13 5 1967 529 539
7. S.H. Cheng, N.J. Higham, C.S. Kenney, and A.J. Laub Approximating the logarithm of a matrix to specified accuracy SIAM Journal on Matrix Analysis and Applications 22 4 2001 1112 1125
8. Chilali, M. (1996). Mthodes LMI pour la synthse multicritre. Ph.D. thesis. Universit de Paris IX Dauphine.
9. Farges, C., Moze, M., & Sabatier, J. (2009). Pseudo state feedback stabilization of commensurate fractional order systems. In European control conference. Budapest, Hungary.
10. Lorenzo, D. F., & Hartley, T. T. (2001). Initialization in fractional order systems. In European control conference. Porto, Portugal (pp. 14711476).
11. Lyapunov, A. (1892). The general problem of the stability of motion. Ph.D. thesis. University of Moscow.
12. Matignon, D. (1996). Stability results on fractional differential equations with applications to control processing. In Computational Engineering in Systems Applications. Vol. 2. Lille, France (pp. 963968).
13. K.S. Miller, and B. Ross An introduction to the fractional calculus and fractional differential equations 1993 John Wiley & Sons
14. Moze, M., Sabatier, J., & Oustaloup, A. (2005). LMI tools for stability analysis of fractional systems. In 20th ASME IEDTC/CIE. Long Beach, California, USA.
15. A. Oustaloup, and B. Mathieu La commande CRONE: du scalaire au multivariable 1999 Herms Paris
16. Sabatier, J., Moze, M., & Farges, C. (2008). On stability of fractional order systems. In Third IFAC workshop on fractional differentiation and its applications FDA'08. Ankara, Turkey.
17. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional integrals and derivatives: theory and applications 1993 Gordon and Breach Science Publishers