论文信息 - Pseudo state feedback stabilization of commensurate fractional order systems

Pseudo state feedback stabilization of commensurate fractional order systems

This paper addresses the problem of pseudo state feedback stabilization of commensurate fractional order systems. In the proposed approach, Linear Matrix Inequalities (LMI) formalism is used to check if the pseudo state matrix eigenvalues belong to the non convex fractional system stability region of the complex plane. A new LMI stability condition is first proposed. Based on this condition, a necessary and sufficient LMI method for the design of stabilizing controllers is given. Its efficiency is evaluated on an inverted fractional pendulum stabilization problem.

Mathieu Moze | Christophe Farges | Jocelyn Sabatier

[1] J. Sabatier,et al. LMI Tools for Stability Analysis of Fractional Systems , 2005 .

[2] Stephen P. Boyd,et al. Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[3] M. Caputo. Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[4] Carl F. Lorenzo,et al. Initialization in fractional order systems , 2001, 2001 European Control Conference (ECC).

[5] Johan Efberg,et al. YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[6] A. M. Lyapunov. The general problem of the stability of motion , 1992 .

[7] D. Matignon. Stability results for fractional differential equations with applications to control processing , 1996 .

[8] A. Oustaloup,et al. La commande crone : du scalaire au multivariable , 1999 .

[9] K. Miller,et al. An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[10] Mathieu Moze,et al. On stability of fractional order systems , 2008 .

[11] Johan Löfberg,et al. YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[12] P. Peres,et al. a linear programming oriented procedure for quadratic stabilization of uncertain systems , 1989 .

[13] Stephen P. Boyd,et al. Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.