Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

Lien, Chang-Hua; Chang, Hao-Chin; Yu, Ker-Wei; Li, Hung-Chi; Hou, Yi-You

doi:10.3390/math9212763

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Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

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Department of Marine Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan

Ph.D. Program of Maritime Science and Technology, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan

Department of Intelligent Commerce, National Kaohsiung University of Science and Technology, Kaohsiung 811, Taiwan

Author to whom correspondence should be addressed.

Academic Editor: Hamid Reza Karimi

Mathematics 2021, 9(21), 2763; https://doi.org/10.3390/math9212763

Received: 11 October 2021 / Revised: 27 October 2021 / Accepted: 28 October 2021 / Published: 30 October 2021

(This article belongs to the Topic Analysis and Controls of Time-Delay Systems with Perturbations: Theory and Application)

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Abstract

In this paper, the mixed performance and reachable set of uncertain discrete systems with slow variation interval time-varying delay are considered. The original uncertain discrete systems with interval time-varying delay are first transformed into a switched system. Then, the proposed improved results are used to guarantee the stability and reachable set of the uncertain system with slow variation interval time-varying delay. The mixed performance (H₂/H_∞) can be derived in the same formulation simultaneously. The design scheme of robust switched control is also developed in this paper. The gains of the controller can be designed and switched to achieve stabilization and mixed performance of the system according to the delay value. Some comparisons with published results are made to show the main contribution of the proposed approach. Finally, some numerical examples are illustrated to show the main results. View Full-Text

Keywords: mixed H₂/H_∞ performance; reachable set; discrete system; slow variation interval time-varying delay

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MDPI and ACS Style

Lien, C.-H.; Chang, H.-C.; Yu, K.-W.; Li, H.-C.; Hou, Y.-Y. Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations. Mathematics 2021, 9, 2763. https://doi.org/10.3390/math9212763

AMA Style

Lien C-H, Chang H-C, Yu K-W, Li H-C, Hou Y-Y. Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations. Mathematics. 2021; 9(21):2763. https://doi.org/10.3390/math9212763

Chicago/Turabian Style

Lien, Chang-Hua, Hao-Chin Chang, Ker-Wei Yu, Hung-Chi Li, and Yi-You Hou. 2021. "Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations" Mathematics 9, no. 21: 2763. https://doi.org/10.3390/math9212763

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Reachable Set and Robust Mixed Performance of Uncertain Discrete Systems with Interval Time-Varying Delay and Linear Fractional Perturbations

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