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Positive Real Lemmas for Fractional-Order Two-Dimensional Roesser Model: The \(0< \rho _1\le 1,0<\rho _2\le 1\) Case

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Abstract

This paper investigates the positive realness of continuous fractional-order (FO) two-dimensional (2D) Roesser model with the FO \(\rho _1\in (0,1],\rho _2\in (0,1]\). A sufficient condition that ensures that the continuous FO 2D Roesser model is stable and positive real is given as linear matrix inequalities (LMIs). Then, the positive real control problem for continuous FO 2D Roesser model with state feedback and dynamic output feedback controllers is addressed. The sufficient conditions are given in LMI form, and the parameters of the controllers can be achieved from the solution of the LMIs easily. Finally, the validity of the results is checked by several examples.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under Grants 62073217.

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Authors and Affiliations

  1. Department of Automation, Shanghai Jiao Tong University, Shanghai, China

    Jia-Rui Zhang & Jun-Guo Lu

  2. Key Laboratory of System Control and Information Processing, Ministry of Education of China, Shanghai, China

    Jia-Rui Zhang & Jun-Guo Lu

  3. Shanghai Engineering Research Center of Intelligent Control and Management, Shanghai, China

    Jia-Rui Zhang & Jun-Guo Lu

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Zhang, JR., Lu, JG. Positive Real Lemmas for Fractional-Order Two-Dimensional Roesser Model: The \(0< \rho _1\le 1,0<\rho _2\le 1\) Case. Circuits Syst Signal Process 43, 2073–2094 (2024). https://doi.org/10.1007/s00034-023-02560-7

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