Observer-based robust control for a class of sampled-data systems with model uncertainty and external disturbance

Abstract

This paper studies the issue of observer-based feedback stabilisation for a class of linear sampled-data systems with model uncertainty and external disturbance. First, for a sampled-data system with external disturbance, a sampled-data observer is designed to estimate the system state. Subsequently, a robust $H_{\mathrm{\infty }}$ controller based on the observer is developed. For a continuous sampling interval, the gain matrices of both observer and controller change exponentially. Second, using the state coordinate transformations with an exponential rate, a unified dynamics is constructed by augmenting the state estimation error and the closed-loop system state as a new state. Next, the sufficient conditions ensuring the asymptotical stability of the closed-loop system are given by the Lyapunov–Krasovskii method and linear matrix inequality (LMI) technique. Finally, the effectiveness of the proposed method is verified by a helicopter model.

Keywords:

• Sampled-data system
• observer
• linear matrix inequality
• robust controller

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Nature Science Foundation of China [grant number 61973105], in part by the Fundamental Research Funds for the Universities of Henan Province [grant number NSFRF180335], in part by the Innovative Scientists and Technicians Team of Henan Provincial High Education [grant number 20IRTSTHN019], in part by the Innovative Scientists and Technicians Team of Henan Polytechnic University [grant number T2019-2], in part by the Innovation Scientists and Technicians Troop Construction Projects of Henan Province [grant number CXTD2016054], and in part by the Zhongyuan high level talents special support plan [grant number ZYQR201912031].

Notes on contributors

Junqi Yang

Junqi Yang received the Ph.D. degree in control theory and control engineering from Tongji University, Shanghai, China, in 2013. He is currently a professor at Henan Polytechnic University. He was a recipient of IJCAS best paper award 2018. His research interests include logical dynamic systems, switched system, observer design, fault detection and tolerant control, etc.

Zechen Li

Zechen Li received his B.S. degree from Wanfang College of Science and Technology, Henan Polytechnic University. He began to pursue his Master's degree at Henan Polytechnic University in 2019. His research interests refer to sampled-data systems, state estimation and fault diagnosis.

Yantao Chen

Yantao Chen received her M.S. degree in control theory and control engineering from China Three Gorges University, Yichang, China, in 2005. She is currently a lecturer at Henan Polytechnic University. Her research interests include parameter estimation and fault-tolerant control.