Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

Yuhan Wang; Xiaodi Li; Shiji Song

doi:10.1109/JAS.2022.105422

Volume 9 Issue 7

Jul. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(7): 1273-1283

Y. H. Wang, X. D. Li, and S. J. Song, “Input-to-state stabilization of nonlinear impulsive delayed systems: An observer-based control approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 7, pp. 1273–1283, Jul. 2022. doi: 10.1109/JAS.2022.105422

Citation:

Y. H. Wang, X. D. Li, and S. J. Song, “Input-to-state stabilization of nonlinear impulsive delayed systems: An observer-based control approach,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 7, pp. 1273–1283, Jul. 2022. doi: 10.1109/JAS.2022.105422

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Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

doi: 10.1109/JAS.2022.105422

Yuhan Wang^1
,,
Xiaodi Li^{2, 3
,
,},
Shiji Song^4
,

1.
School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China
2.
School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China
3.
School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China
4.
Department of Automation, Tsinghua University, Beijing 100084, China

Funds: This work was supported by the National Natural Science Foundation of China (62173215), Major Basic Research Program of the Natural Science Foundation of Shandong Province in China (ZR2021ZD04, ZR2020ZD24), and the Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions (2019KJI008)

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Author Bio:
Yuhan Wang (Student Member, IEEE) received the B.S. degree from the School of Mathematics and Statistics, Shandong Normal University, in 2018. He is currently a Master student in control theory at the School of Mathematics and Statistics, Shandong Normal University. His research interests include stability theory, observer issues, neural networks, and impulsive control theory

Xiaodi Li (Member, IEEE) received the B.S. and M.S. degrees from Shandong Normal University, in 2005 and 2008, respectively, and the Ph.D. degree from Xiamen University, in 2011, all in applied mathematics. He joined the School of Mathematics and Statistics, Shandong Normal University in 2011. He is currently a Professor and the Director of the Research Center for Control and Engineering Computation. From May 2019, he is the Dean of the School of Mathematics and Statistics, Shandong Normal University. From Nov. 2014 to Dec. 2016, he was a Visiting Research Fellow at Laboratory for Industrial and Applied Mathematics in York University, Canada, and the University of Texas at Dallas, USA. From 2017 to 2019, he was a Visiting Research Fellow at the Department of Mathematics in City University of Hong Kong, and the Department of Mechanical Engineering in The University of Hong Kong, China, respectively. His current research interests include discontinuous control theory, delay systems, hybrid systems, artificial neural networks, and applied mathematics. He has been a recipient of the Highly Cited Researchers Award by Clarivate Analytics in 2020 and 2021, and also the China’s high-cited scholars since 2014. He is currently the Editor-in-Chief of Mathematical Modelling and Control, the Subject Editor of Applied Mathematical Modelling, the Associate Editor of International Journal of Systems Science, Neural Processing Letters, etc. He has authored or coauthored more than 100 research papers

Shiji Song (Senior Member, IEEE) received the B.S. degree in mathematics from Harbin Normal University in 1986, and the M.S. and Ph.D. degrees in mathematics from Harbin Institute of Technology in 1989 and 1996, respectively. Since 2000, he has been with the Department of Automation, Tsinghua University, where he is currently a Professor. His research and teaching interests include system identi- fication, stochastic neural networks, reinforcement learning, and visual information systems for ocean mineral resources and applications. He has published in various well-established journals, including the IIE Transactions, Journal of Scheduling, European Journal of Operational Research, Journal of the Operational Research Society, IEEE Transactions on Neural Networks and Learning Systems, and IEEE Transactions on Circuits and Systems
Corresponding author: Xiaodi Li, e-mail: lxd@sdnu.edu.cn
Received Date: 2021-11-15
Accepted Date: 2021-12-10

Available Online: 2022-01-08

Abstract

Abstract

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis- turbances. Since the information of plant’s states, time delays, and exogenous disturbances is often hard to be obtained, the key design challenge, which we resolve, is the construction of a state observer-based controller. For this purpose, we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct (or estimate) the plant’s states. And then based on the observations, we establish an observer-based control design for the plant to achieve the input-to-state stability (ISS) and integral-ISS (iISS) properties. With the help of the comparison principle and average impulse interval approach, some sufficient conditions are presented, and moreover, two different linear matrix inequalities (LMIs) based criteria are proposed to design the gain matrices. Finally, two numerical examples and their simulations are given to show the effectiveness of our theoretical results.
- Average impulse interval,
- input-to-state stabilization (ISS),
- nonlinear impulsive systems,
- observer-based control,
- time delays

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References(43)

References

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The problems of input-to-state stabilization for impulsive delayed systems are addressed
A novel observer-based output feedback controller is designed for stabilization
The designed state observer can be applied to the case involving unmeasurable time delays
Two different design schemes for controller are proposed in terms of linear matrix inequalities

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

doi: 10.1109/JAS.2022.105422

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