The controller design for singular fractional-order systems with fractional order \(0 < \alpha< 1\)

Abstract

We study the problem of pseudostate and static output feedback stabilization for singular fractional-order linear systems with fractional order \(\alpha \) when \(0 <\alpha < 1\). All the results are given by linear matrix inequalities. First, a new sufficient and necessary condition for the admissibility of singular fractional-order systems is presented. Then based on the admissible result, not only are sufficient conditions for designing pseudostate and static output feedback controllers obtained, but also sufficient and necessary conditions are presented by using different methods that guarantee the admissibility of the closed-loop systems. Finally, the effectiveness of the proposed approach is demonstrated by numerical simulations and a real-world example. doi:10.1017/S1446181118000202