Dynamic observer-based control for fractional-order uncertain linear systems

This paper addresses the problem of dynamic observer-based control for fractional-order linear uncertain systems. By constructing a new linearising change of variables, the conditions for designing the observer and controller gains are obtained in terms of solutions to a set of linear matrix inequalities (LMIs) even in the presence of uncertainties in system, input and output matrices simultaneously. Meanwhile, owing to having additional degrees of freedom in the designed observer structure, the proposed methods have no equality constraint, which is needed by using Luenberger-type observer. Numerical examples are given to illustrate the benefits and the effectiveness of the proposed method.