Tracking control of discrete-time Markovian jump systems

Abstract

This paper is concerned with the model reference tracking control (MRTC) problem of discrete-time Markovian jump systems under external disturbance and input constraints. A state feedback controller is proposed to guarantee that the state vector of the system tracks precisely a given state vector of a reference model. The tracking problem is formulated as an optimisation problem and an approach to design the state feedback controller which stabilises the augmented system and rejects the external disturbance simultaneously. Sufficient conditions for stochastic stability and stabilisation of the augmented systems are derived via linear matrix inequalities. Then, under the assumption of completely unknown system modes, a common MRTC approach is developed to guarantee the stochastic stability, the disturbance rejection and the input constraints. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method.

Keywords:

• Discrete-time
• Markovian jump systems
• tracking control
• state feedback
• linear matrix inequality (LMI)

Disclosure statement

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

Additional information

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: this work was supported by the Major Program of National Natural Science Foundation of China [Grant Numbers 61690210, 61690212], and by the National Natural Science Foundation of China [61333003].

Notes on contributors

Guangtai Tian

Guangtai Tian received his B.Sc. degree from the Department of Mechanical Engineering at Nanjing University of Science andTechnology (NUST), Nanjing, China in 2017. He is currently a Ph.D. student in Harbin Institute of Technology (HIT). His research interestsinclude robust control, tracking control, and linear systems.