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Static and Dynamic Output Feedback Control for Polytopic Uncertain Fractional Order Systems with 0 < μ < 1

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  • Control Theory and Applications
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Abstract

The stabilization conditions of fractional order systems (FOS) with order 0 < μ < 1 via two different types of output feedback controls are discussed in this paper. Firstly, by using variable substitution, an alternative condition that guarantees autonomous FOS to be asymptotically stable is proposed, the condition contains only a single variable. Then, based on this stability criterion, the stabilization conditions for FOS and polytopic FOS are given in the form of direct linear matrix inequality. And the obtained results can overcome some drawbacks in the existing work. Furthermore, we extend the results to the singular fractional order case. Finally, the effectiveness of the results is verified by numerical examples.

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Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, Liaoning, 110819, China

    Xuefeng Zhang & Zerui Han

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  1. Xuefeng Zhang
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  2. Zerui Han
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Correspondence to Xuefeng Zhang.

Additional information

Xuefeng Zhang received his B.Sc. degree in applied mathematics, an M.S. degree in control theory and control engineering, and a Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 1989, 2004, and 2008, respectively, where he is currently with the College of Sciences. He has published more than 100 journal and conference papers and 3 books. He is the Associate Editors of IEEE Access and Fractal and Fract and the Committee member of Technical Committee on Fractional and Control of Chinese Association of Automation. His research interests include fractional order control systems and singular systems.

Zerui Han received her B.Sc. degree in mathematics and applied mathematics from Inner Mongolia University in 2018. She is currently pursuing an M.S. degree in operations research and cybernetics with Northeastern University, Shenyang, China, where she is also with the College of Sciences. Her research interests include fractional order systems, singularly perturbed systems, and feedback control.

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This work was supported by the Chinese National Key research and development program (2020YFB1710003).

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Zhang, X., Han, Z. Static and Dynamic Output Feedback Control for Polytopic Uncertain Fractional Order Systems with 0 < μ < 1. Int. J. Control Autom. Syst. 21, 52–60 (2023). https://doi.org/10.1007/s12555-021-0416-2

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  • DOI: https://doi.org/10.1007/s12555-021-0416-2

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