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

Tao Zhan, Shuping Ma


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.



admissibility, feedback control, singular fractional-order systems, linear matrix inequalities.


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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.