Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties

Robust stability and stabilization of fractional-order uncertain linear systems with order α:0<α<1 and 1⩽α<2 are considered in the paper. A new polytopic type uncertain state-space model for fractional-order linear systems is addressed, which allows second-order uncertain parameters. The uncertainty in the fractional-order model appears in terms of a polytope of matrices. Some sufficient criteria for the robust asymptotical stable and stabilization for such fractional-order uncertain linear systems are derived. All the results are obtained in terms of linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the validity and feasibility of the obtained results.