Delay-dependent decentralised control for a class of uncertain similar interconnected systems with state delay and input delay

Abstract

In this paper, the problem of delay-dependent decentralised control for a class of uncertain similar interconnected systems is investigated, where not only the state vectors but also the input vectors involve time delay. The new similar structure is presented via state feedback, based on which, by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised stabilization controllers are designed, which is dependent on time delays, to stabilise the interconnected systems uniformly asymptotically. The results show that the design is easy to calculate and the controllers have the similar structure, so it is easy to realise project. Finally, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.

Keywords:

• decentralised control
• similar structure
• delay-dependent
• interconnected systems

Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their many helpful comments and suggestions to improve the quality of this paper.

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China, under [grant number 61273004].

Notes on contributors

Yuechao Ma

Yuechao Ma received his BS degree from Northeast Normal University, Changchun, P.R. China in 1984 and MS degree from Chinese Academy of Science, Beijing, P.R. China, in 1988. He was awarded a PhD degree in Northeastern University, Shenyang, P.R. China in 2006. Currently, he is a professor in the Yanshan University. His research interests include decentralised control, chaos control, descriptor systems and so on.

Shujie Jin

Shujie Jin received her BS degree in Mathematics from Baoding College, Hebei, P.R. China, in 2011 and the MS degree in Mathematics from Yanshan University, Hebei, P.R. China, in 2013. Her current research interest is mainly on control design of nonlinear interconnected systems.

Nannan Gu

Nannan Gu received her BS degree in Mathematics from Baoding College, Hebei, P.R. China, in 2011 and the MS degree in Mathematics from Yanshan University, Hebei, P.R. China, in 2013. Her current research interest is mainly on control design of discrete-time descriptor systems.