Robust stability analysis and stabilization of fractional order polytopic systems

This paper addresses the problem of robust pseudo state feedback stabilization 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 whatever the value of the uncertain parameters. The paper focuses particularly on the case 0 < nu < 1 as the stability region is non convex and associated LMI condition is not as straightforward to obtain as in the case 1 < nu < 2. The quadratic stabilisation problem involving a single matrix in order to prove stability of the closed loop system is first addressed. Additional variables are then introduced in order to decouple system matrices from the ones proving stability of the closed loop system. This decoupling allows using parameter dependant stability matrices and leads to less conservative results as attested by a numerical example.