L₂-L_∞ filtering for stochastic delayed systems with randomly occurring nonlinearities and sensor saturation

Abstract

This work investigates L₂-L_∞ filtering problem for a class of stochastic systems with time-delay and randomly occurring phenomena. The purpose of the addressed problem is to design a full order filter to ensure the filtering error system is asymptotically mean-square stable with prescribed L₂-L_∞ performance. A novel stochastic time-delay system model is established, in which randomly occurring nonlinearities and sensor saturation phenomena are considered. Then, a novel functional containing negative definite terms is constructed to relax the constraints on the functional, and a new free-matrix-based stochastic integral inequality is also given. Meanwhile, a novel L₂-L_∞ performance analysis method making full use of delay information is proposed. As a result, less conservative conditions for the existence of filters are obtained, under which the L₂-L_∞ performance level can be achieved for the filtering error system. Numerical examples are employed to show the benefits of the proposed approach.

KEYWORDS:

• Stochastic delayed system
• randomly occurring
• incomplete information
• stochastic integral inequality
• L₂-L_∞ filtering

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of PR China under Grants 61573130 and 61973105, in part by the Innovation Scientists and Technicians Troop Construction Projects of Henan Province under Grant CXTD2016054, Zhongyuan high level talents special support plan under Grant ZYQR201912031, the Fundamental Research Funds for the Universities of Henan Province under Grant NSFRF170501.

Notes on contributors

Wei Qian

Wei Qian received the Ph.D. degree from the State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China, in 2009. He is currently a Professor with the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. His current research interests include time-delay systems, stochastic systems, networked control systems, and multiagent system.

Yujie Li

Yujie Li received his B.E. degree in automation from Henan University of Urban Construction in 2015. She is currently a Master degree candidate at the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. Her research interests include state estimation and filtering for time-delay systems and stochastic systems.

Yonggang Chen

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

Wei Liu

Wei Liu received his M.S. degree in control theory and control engineering from University of Science and Technology Liaoning, Anshan, China, in 2006, and received his Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China, in 2011. Presently, he is an associate professor in the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. His main research interests include estimation theory, multiple model estimation and linear-quadratic-Gaussian control. He is a Senior Member of the Institute of Electrical and Electronic Engineers.