Stabilising control for impulsive systems

Abstract

This paper is aimed at stabilising control for impulsive systems via the state feedback. Firstly, stability analysis for the closed-loop system is conducted using a Lyapunov-like functional (LLK) that is not necessarily continuous nor positive definite. Built on two subintervals of the impulsive interval being separated by the current instant, a concrete LLK is constructed by introducing multiple integrals of the state and cross terms among the integrals, the state and impulsive states. Integral equations of the impulsive system are exploited and high-order integral inequalities are taken when estimating the derivative of the LLK. New stability results with interval dwell-time, maximal dwell-time or minimal dwell-time are obtained. Secondly, based on the stability results the stabilising control problem is solved via linear matrix inequality approach. Finally, numerical examples illustrate that the stability results are less conservative and the control for impulsive systems is valid.

KEYWORDS:

• Impulsive systems
• stability analysis
• stabilising control

Disclosure statement

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

Data availability statement

There is not a data set associated with this paper.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 62373214].

Notes on contributors

Lin Shao

Lin Shao received his bachelor's degree in communication engineering from Northwestern Polytechnical University in 2011. In 2018, he received the Ph.D. degree in electronic science and technology from Beijing University of Posts and Telecommunications. After graduation, he joined the College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao, China. His research interests include signal processing, wireless communication system and neural networks.Professor Hanyong Shao received the M.S. degree in operational research and control theory from Qufu Normal University, Qufu, China, and the Ph.D. degree in control theory and engineering from Southeast University, Nanjing, China, in 1997 and 2005, respectively.In 1997, he joined the School of Electrical and Information Automation, Qufu Normal University, Rizhao, Shandong, China, where he is currently a Professor. In 2009 he was a research associate in Centre for Intelligent and Networked Systems, Central Queensland University, Australia. In 2013 he was a visiting professor in the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. His research interests include systems and signal processing, networked control systems, time-delay systems, neural networks and robust control.