Novel admissibility and robust stabilization conditions for fractional-order singular systems with polytopic uncertainties

This paper considers the issues of the admissibility and robust stabilization of fractional-order singular systems with polytopic uncertainties and fractional-order & alpha;:1 & LE;& alpha;<2$$ \alpha :1\le \alpha and 0<& alpha;<1$$ 0. Firstly, the novel admissibility conditions for nominal fractional-order singular systems are proposed with no conservatism and without any equalities or nonstrict inequalities. Secondly, the robust admissibility conditions for fractional-order singular systems with polytopic uncertainties are given based on the admissibility conditions for nominal fractional-order singular systems. Thirdly, to make the uncertain fractional-order singular systems robustly admissible, the methods of designing the static output feedback controllers are obtained with wider application scope, which are direct, concise, and more relaxed compared with the existing results. All the results are proposed in terms of linear matrix inequalities. Finally, three illustrative examples are given to demonstrate the effectiveness of the results.

Automated summary

This paper considers the admissibility and robust stabilization issues of fractional-order singular systems with polytopic uncertainties. Novel admissibility conditions for nominal fractional-order singular systems are proposed. Robust admissibility conditions for fractional-order singular systems with polytopic uncertainties are given based on the admissibility conditions for nominal fractional-order singular systems. Methods of designing static output feedback controllers that make the uncertain fractional-order singular systems robustly admissible are obtained. The results are illustrated with three examples.