Static and Dynamic Output Feedback Control for Polytopic Uncertain Fractional Order Systems with 0 < μ < 1

The stabilization conditions of fractional order systems (FOS) with order 0 < μ < 1 via two different types of output feedback controls are discussed in this paper. Firstly, by using variable substitution, an alternative condition that guarantees autonomous FOS to be asymptotically stable is proposed, the condition contains only a single variable. Then, based on this stability criterion, the stabilization conditions for FOS and polytopic FOS are given in the form of direct linear matrix inequality. And the obtained results can overcome some drawbacks in the existing work. Furthermore, we extend the results to the singular fractional order case. Finally, the effectiveness of the results is verified by numerical examples.