Fractional order polytopic systems: robust stability and stabilisation

Abstract : This article addresses the problem of robust pseudo state feedback stabilisation of commensurate fractional order polytopic 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 domain whatever the value of the uncertain parameters. The article focuses particularly on the case of a fractional order ν such that 0 < ν < 1, as the stability region is non-convex and associated LMI condition is not as straightforward to obtain as in the case 1 < ν < 2. In relation to the quadratic stabilisation problem previously addressed by the authors and that involves a single matrix to prove stability of the closed loop system, additional variables are then introduced to decouple system matrices in the closed loop system stability condition. This decoupling allows using parameter-dependent stability matrices and leads to less conservative results as attested by a numerical example.
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Christophe Farges, Jocelyn Sabatier, Mathieu Moze. Fractional order polytopic systems: robust stability and stabilisation. Advances in Difference Equations, SpringerOpen, 2011, ⟨10.1186/1687-1847-2011-35⟩. ⟨hal-00676079⟩

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