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This study analyzes the H∞$$ {H}_{\infty } $$ model reduction methods and the robust H∞$$ {H}_{\infty } $$ model reduction methods for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser system with the FO ranging from 0 to 1. A sufficient LMI‐based condition is given by Projection Lemma, the FO‐stable‐region‐analyze method and matrix analysis, guaranteeing that the error system is stable and that its transfer function's H∞$$ {H}_{\infty } $$‐norm is bounded. Then, the approach to design the reduced‐model system of the original continuous FO 2D Roesser model is given. The robust H∞$$ {H}_{\infty } $$ model reduction methods for continuous FO 2D Roesser systems with polytopic uncertainties are proposed based on the results above. In the end, two numerical examples are used to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

This paper considers the issues of the admissibility and robust stabilization of fractional‐order singular systems with polytopic uncertainties and fractional‐order α:1≤α<2$$ \alpha :1\le \alpha <2 $$ and 0<α<1$$ 0<\alpha <1 $$. 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. [ABSTRACT FROM AUTHOR]

This paper investigates the admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties. Firstly, based on the analysis of the regularity, causality and stability, novel admissibility conditions for nominal fractional-order singular discrete systems are derived including a necessary and sufficient condition in terms of spectral radius and a sufficient condition in terms of non-strict linear matrix inequalities. In order to eliminate the coupling terms and propose strict linear matrix inequality results, another novel admissibility condition is obtained, which is more tractable and reliable with the available linear matrix inequality software solver and more suitable for the controller design compared with the existing results. Secondly, the state feedback controller synthesis for the fractional-order singular discrete systems with interval uncertainties is addressed and the state feedback controller is designed. Finally, the efficiency of the proposed method is demonstrated by two numerical simulation examples. [ABSTRACT FROM AUTHOR]

This paper investigates the H∞$$ {H}_{\infty } $$ filtering for the continuous fractional‐order (FO) two‐dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of H∞$$ {H}_{\infty } $$‐norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the H∞$$ {H}_{\infty } $$ filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples. [ABSTRACT FROM AUTHOR]