Input–output finite-time stabilisation of Markovian jump systems with incomplete transition rates: a sliding mode method

ABSTRACT

In this paper, the input–output finite-time stabilisation (IO-FTS) problem for a class of Markovian jump systems is investigated, in which some elements in the transition rate matrix are partially known and an explicit output constraint condition is required, i.e. the system output (weighted) norm does not exceed an assigned threshold β. An extended definition of IO-FTS is firstly given to reduce the conservativeness arising from zero initial condition $x\left(0\right)=0$. A parameter-dependent sliding mode control strategy is proposed to eliminate the effect of partially known transition rates such that state trajectories are driven to the specified sliding surface during a given finite (possibly short) time interval. Besides, the sufficient conditions are derived to ensure the IO-FTS of the closed-loop systems over the finite-time interval including the reaching phase and the sliding motion phase. Finally, a simulation example illustrates the validity of the proposed method.

Keywords:

• Markovian jump systems
• incomplete transition rates
• input–output finite-time stability
• sliding mode control

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation [61673174] and 111 Project [B17017] from China.

Notes on contributors

Zhiru Cao

Zhiru Cao received the B.S. degree from Nanjing Tech University, China, in 2016. She is now pursuing her Ph.D. degree in Control Science & Engineering at East China University of Science and Technology, China. Her current research areas are Markovian jump systems, sliding mode control, and finite-time control.

Yugang Niu

Yugang Niu is a professor with the East China University of Science & Technology. His research Areas includes sliding mode control, stochastic systems, wireless sensor networks, microgrid.

Tinggang Jia

Tinggang Jia received his PhD degrees from the East China University of Science & Technology in 2012. Now, he is a professor of Engineering inIndustrial Automation and Control Science and Engineering of Shangha iElectric Group Co., Ltd. His current research interests include automation control and application, robust control and networked control systems.