Stability analysis and design of cooperative control for linear delta operator system

Yanmei Xue; Jinke Han; Ziqiang Tu; Xiangyong Chen; Yanmei Xue; Jinke Han; Ziqiang Tu; Xiangyong Chen

doi:10.3934/math.2023637

AIMS Mathematics

2023, Volume 8, Issue 6: 12671-12693. doi: 10.3934/math.2023637

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Research article

Stability analysis and design of cooperative control for linear delta operator system

1.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, Jiangsu, China
2.
School of Automation and Electrical Engineering, Linyi University, Linyi 276000, Shandong, China
3.
School of Mathematical and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China

Received: 18 January 2023 Revised: 18 March 2023 Accepted: 20 March 2023 Published: 29 March 2023
MSC : 93A15

This paper investigates the cooperative state feedback control problem for delta operator-based large-scale systems with independent subsystems. First, the state feedback controller is introduced to interconnect the adjacent subsystems into a closed-loop system. Second, the Lyapunov function in delta domain is constructed, and the linear matrix inequality method is used to design the cooperative state feedback stability controller for the whole large-scale interconnected system. Third, a performance index is introduced for the design of the optimal cooperative state feedback controller. Finally, stability of the closed-loop system is proved on the basis of stability theory, and simulation examples are given for showing the effectiveness of the design method.
- delta operator,
- interconnected systems,
- cooperative control,
- stability analysis
Citation: Yanmei Xue, Jinke Han, Ziqiang Tu, Xiangyong Chen. Stability analysis and design of cooperative control for linear delta operator system[J]. AIMS Mathematics, 2023, 8(6): 12671-12693. doi: 10.3934/math.2023637

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Abstract

This paper investigates the cooperative state feedback control problem for delta operator-based large-scale systems with independent subsystems. First, the state feedback controller is introduced to interconnect the adjacent subsystems into a closed-loop system. Second, the Lyapunov function in delta domain is constructed, and the linear matrix inequality method is used to design the cooperative state feedback stability controller for the whole large-scale interconnected system. Third, a performance index is introduced for the design of the optimal cooperative state feedback controller. Finally, stability of the closed-loop system is proved on the basis of stability theory, and simulation examples are given for showing the effectiveness of the design method.

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