LMI stability conditions for fractional order systems

Authors:
Jocelyn Sabatier;Mathieu Moze;Christophe Farges
Affiliations:
IMS Laboratory, LAPS/CRONE Group, CNRS UMR 5218, Bordeaux 1 University, 351 cours de la libération, 33405 Talence, France;IMS Laboratory, LAPS/CRONE Group, CNRS UMR 5218, Bordeaux 1 University, 351 cours de la libération, 33405 Talence, France;IMS Laboratory, LAPS/CRONE Group, CNRS UMR 5218, Bordeaux 1 University, 351 cours de la libération, 33405 Talence, France
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

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 @n is such that 0