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Zbl 1189.34020
Sabatier, Jocelyn; Moze, Mathieu; Farges, Christophe
LMI stability conditions for fractional order systems. (English)
[J] Comput. Math. Appl. 59, No. 5, 1594-1609 (2010). ISSN 0898-1221

Summary: After an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives, also denoted fractional order systems, this paper deals with Linear Matrix Inequality (LMI) stability conditions for fractional order systems. Under commensurate order hypothesis, it is shown that a direct extension of the second Lyapunov's method is a tedious task. If the fractional order $\nu $ is such that $0<\nu <1$, the stability domain is not a convex region of the complex plane. However, through a direct stability domain characterization, three LMI stability analysis conditions are proposed. The first one is based on the stability domain deformation and the second one on a characterization of the instability domain (which is convex). The third one is based on generalized LMI framework. These conditions are applied to the gain margin computation of a CRONE suspension.

MSC 2000:: *34A33
34D20 Lyapunov stability of ODE
93D20 Asymptotic stability of control systems
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional systems; stability; linear matrix inequalities

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