LMI stability conditions for fractional order systems. (English) Zbl 1189.34020

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.


34A33 Ordinary lattice differential equations
34D20 Stability of solutions to ordinary differential equations
93D20 Asymptotic stability in control theory
26A33 Fractional derivatives and integrals


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