Robust stabilization of uncertain descriptor fractional-order systems

International audience; This paper presents sufficient conditions for the robust asymptotical stabilization of uncertain descriptor fractional-order systems with the fractional order α satisfying 0 < α < 2. The results are obtained in terms of linear matrix inequalities. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in the state matrix. A necessary and sufficient condition for the normalization of uncertain descriptor fractional-order systems is given via linear matrix inequality (LMI) formulation. The state feedback control to robustly stabilize such uncertain descriptor fractional-order systems with the fractional order α belonging to 0 < α < 2 is derived. Two numerical examples are given to demonstrate the applicability of the proposed approach.