Observer-based passive control of non-homogeneous Markov jump systems with random communication delays

ABSTRACT

This paper focuses on the passive control problem for Markov jump systems with piecewise-constant transition rates, random nonlinearities and random communication delays. An observer is used to obtain the system state, and communication delay with probabilistic distribution is considered. The probabilistic properties of the nonlinear perturbations and communication delays are described by two mutually independent Bernoulli sequences. Based on average dwell time method and Lyapunov stability theory, a sufficient stochastic passivity condition is presented. By singular value decomposition technique the gain matrices can be computed via strict linear matrix inequalities, and the desired controller guarantees the stochastic passivity of the closed-loop augmented system. The effectiveness of the method is illustrated by a numerical example.

Keywords:

• Markov jump systems
• piecewise-constant transition probability
• observer
• passivity
• random communication delays

Acknowledgements

This work was supported partially by the Zhejiang Provincial Natural Science Foundation of China under grant LR16F030003, and partially by the National Natural Science Foundation of China under grants U1509205, 61973102 and 61427808.

Disclosure statement

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

Additional information

Funding

This work was supported partially by the Zhejiang Provincial Natural Science Foundation of China under Grant Number LR16F030003, and partially by the National Natural Science Foundation of China under Grant Numbers U1509205, 61973102 and 61427808.

Notes on contributors

Yun Chen

Yun Chen was born in Zhejiang Province, China. He received the Ph.D. degree in Control Science and Engineering in 2008, from Zhejiang University, Hangzhou, China. In 2002, he joined Hangzhou Dianzi University, Hangzhou, China, where he is currently a Professor. His research interests include stochastic and hybrid systems, robust control and filtering.

Zhangping Chen

Zhangping Chen was born in Zhejiang Province, China, in 1987. He received the M.S. degree from Hangzhou Dianzi University, Hangzhou, China, in 2013. He is currently pursing toward the Ph.D. degree in Control Science and Engineering with School of Automation, Hangzhou Dianzi University, Hangzhou, China. His research interests include stochastic systems analysis and synthesis, robust control, and embedded applications.

Zhenyu Chen

Zhenyu Chen was born in Fujian province, China, in 1993. He received the M.S. degree from Hangzhou Dianzi University, Hangzhou, China, in 2019. He is now with Software Development Center, China Merchants Bank, Hangzhou, China. His research interests include networked control systems, Markov jump systems.

Anke Xue

Anke Xue received the Ph.D. degree in Control Science and Engineering from Zhejiang University, Hangzhou, China, in 1997. He is currently a full Professor with Hangzhou Dianzi University, Hangzhou, China. His research interests cover robust control theory and applications.