Anti-disturbance control for time-varying delayed semi-Markovian jump systems with saturation and generally uncertain transition rates via disturbance observer

Abstract

The issue of anti-disturbance control for semi-Markovian jump systems (S-MJSs) with saturation via disturbance observer is investigated in this paper. Compared with the existing results, time-varying delay, actuator saturation, exogenous disturbance and generally uncertain transition rates are all considered in S-MJSs. Firstly, the sufficient condition of stochastic stability based on S-MJSs with time-varying delay is proposed by stochastic Lyapunov–Krasovskii functional. Secondly, disturbance observer-based control is applied in S-MJSs for addressing exogenous disturbance, and the controller is designed to guarantee the system performance. After that, the maximum estimation of domain of attraction is solved by an optimisation problem. Finally, two practical cases are introduced for testifying the accuracy of the proposed methods.

Keywords:

• Semi-Markovian jump systems
• time-varying delay
• actuator saturation
• disturbance observer-based control

Disclosure statement

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

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61573088].

Notes on contributors

Tianbo Xu

Tianbo Xu is a Ph.D. candidate in the College of Information Science and Engineering at Northeastern University. He received the B.S. degree in Electronic information engineering at Shenyang University of Technology in 2009, and received the two M.S. degree: control engineering from Northeastern University in 2015, safety engineering from China University of Petroleum in 2018. His research interests are semi-Markovian jump systems, anti-disturbance control, deep learning and so on.

Xianwen Gao

Xianwen Gao is a Professor in the College of Information Science and Engineering at Northeastern University. He received B.S. degree from Shenyang University of Chemical Technology in 1978 and received M.S. degree from Northeastern University in 1993. In 1998, he received Ph.D. degree in control theory and and control engineering from Northeastern University. His research interests are modelling of complex industry process and intelligent control, stochastic jump systems and so on.

Wenhai Qi

Wenhai Qi was born in Taian, China, in 1986. He received the B.S. degree in automation and the M.S. degree from Qufu Normal University in 2008 and 2013, respectively, and the Ph.D. degree in control theory and control engineering from Northeastern University in 2016. He is currently with the School of Engineering, Qufu Normal University, Rizhao, China. His research focus on Markovian jump systems, switched systems, positive systems, networked control systems and so on.