Robust stability for fractional-order systems with structured and unstructured uncertainties

The issues of robust stability for uncertain fractional-order systems of two types of order α∈(0,1)α∈(0,1) are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition for robust stability is given; for the norm-bounded uncertainty case, a sufficient and necessary condition for robust stability is presented. Both of these conditions can be checked by solving sets of linear matrix inequalities. Two numerical examples are presented to confirm the proposed conditions.