Pseudo-state feedback stabilization of commensurate fractional order systems

Abstract : This paper addresses the problem of pseudo-state feedback stabilization of commensurate fractional order systems (FOS). In the proposed approach, Linear Matrix Inequalities (LMI) formalism is used to check if the pseudo-state matrix eigenvalues belong to the FOS stability region of the complex plane. A review of LMI stability conditions is first proposed for fractional order 0 < alpha < 1 and 1 < alpha < 2. The paper then focuses particularly on the case 0 < alpha < 1 as the stability region is non-convex and associated LMI condition is not as straightforward to obtain as in the case 1 < alpha < 2. A new LMI stability condition is thus proposed. Based on this condition, a necessary and sufficient LMI method for the design of stabilizing controllers is given. This method paves the way for extension to FOS of various LMI-based results. Among these possible extensions, a first result on robust control of polytopic fractional order systems is given in this paper.
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Submitted on : Wednesday, November 3, 2010 - 6:30:14 PM
Last modification on : Thursday, January 11, 2018 - 6:21:07 AM

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Christophe Farges, Mathieu Moze, Jocelyn Sabatier. Pseudo-state feedback stabilization of commensurate fractional order systems. Automatica, Elsevier, 2010, 46 (10), pp.1730-1734. ⟨10.1016/j.automatica.2010.06.038⟩. ⟨hal-00531790⟩

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