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Regional Stabilization for Linear Time-delay Systems Under Amplitude and Rate Saturations of Actuators

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  • Control Theory and Applications
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Abstract

This paper considers the regional stabilization problem for linear time-delay systems under amplitude and rate saturations of physical actuators. First of all, a position-type first-order model is utilized to represent physical actuators, and the distributed-delay-dependent sector conditions are proposed to deal with the saturation nonlinearities. Then, based on the Lyapunov-Krasovskii approach, sufficient conditions are established in the framework of linear matrix inequalities under which the regional stability of the closed-loop systems can be guaranteed. Moreover, the optimization problems about the stability region are formulated. In addition, the further discussions are provided for the cases with uncertainties and disturbances. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, 453003, China

    Yuanyuan Bai, Yonggang Chen & Nannan Zhang

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  1. Yuanyuan Bai
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  2. Yonggang Chen
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Correspondence to Yonggang Chen.

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This work was supported in part by the National Natural Science Foundation of China under Grant 62273132, in part by the Natural Science Foundation of Henan Province of China under Grant 202300410159, and in part by the Natrual Science Foundation of Shandong Province of China under Grant ZR2017LF010.

Yuanyuan Bai received her B.Sc. degree in mathematics from Henan Institute of Science and Technology, Xinxiang, China, in 2020. She is currently working toward an M.Sc. degree in system sciences from Henan Institute of Science and Technology, Xinxiang, China. Her research interests are constrained control and time-delay systems.

Yonggang Chen received his B.Sc. and M.Sc. degrees in mathematics from Henan Normal University, Xinxiang, China, in 2003 and 2006, respectively. He received a Ph.D. degree in control theory and control engineering from Southeast University, Nanjing, China, in 2013. He is currently a professor with the School of Mathematical Sciences of Henan Institute of Science and Technology, Xinxiang, China. His research interests include time-delay systems, constrained control, networked control, and switched control.

Nannan Zhang received her B.Sc. degree in mathematics from Henan Institute of Science and Technology, Xinxiang, China, in 2020. She is currently working toward an M.Sc. degree in system sciences from Henan Institute of Science and Technology, Xinxiang, China. Her research interests are time-delay systems and neural networks.

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Bai, Y., Chen, Y. & Zhang, N. Regional Stabilization for Linear Time-delay Systems Under Amplitude and Rate Saturations of Actuators. Int. J. Control Autom. Syst. 21, 865–875 (2023). https://doi.org/10.1007/s12555-021-0896-0

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  • DOI: https://doi.org/10.1007/s12555-021-0896-0

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