Dynamic anti-windup design for linear systems with time-varying state delay and input saturations

Abstract

This paper considers the dynamic anti-windup design problem for linear systems with time-varying state delay, input saturations and external disturbances. A dynamic anti-windup compensator is first designed that is dependent on the upper bound of the time-varying delay. Then, using an augmented Lyapunov–Krasovskii functional, a distributed-delay-dependent sector condition, some advanced inequalities and some congruence transformations, sufficient conditions are established under which the state trajectories of the closed-loop systems are bounded and meanwhile, the $H_{\mathrm{\infty }}$ performance can be guaranteed. The anti-windup compensator gain can be explicitly solved by means of linear matrix inequalities. For the case of constant delay, the corresponding result is also presented. Finally, two numerical examples illustrate the effectiveness and advantages of the proposed results.

Keywords:

• Dynamic anti-windup
• linear systems
• time-varying state delay
• input saturations

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61773156] and the Natural Science Foundation of Henan Province of China [grant number 202300410159].

Notes on contributors

Yonggang Chen

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 his 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, switched control and so on.

Kunbao Ma

Kunbao Ma received his B.Sc. degree in Mathematics from Henan Institute of Science and Technology, Xinxiang, China, in 2019. He is perusing his M.Sc. degree in System Science from Henan Institute of Science and Technology, Xinxiang, China. His research interests are time-delay systems and constrained control.

Rui Dong

Rui Dong received her B.S. degree in mathematics from Xinyang Normal University, in 1995, M.S. degree in mathematics from Henan Normal University, in 2004, and Ph.D. degree in ocean information detection and processing from the Ocean University of China, Qingdao, China, in 2008. She is currently a professor with the School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang, China. Her research interests include system control, game theory and social networks.