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ABSTRACT
This paper is concerned with the robust stabilsation of uncertain delayed Markovian jump systems. Given a Markovian jump system with time delay and Brownian motion simultaneously, we allow the uncertainty added in the form of additive perturbations and existing in the drift and diffusion sections at the same time. A sufficient condition on the mean square stability of system in the face of such disturbances is obtained, which is similar to small-gain theorem. A kind of partially delay-dependent controller stabilising the resulting closed-loop system is firstly designed to relate to the probability distribution of delay, whose key idea is applied to construct a delayed controller with disordering phenomenon. It is seen that the existence conditions established here could be solved easily. Based on the proposed results, some applications on robust synchronisation of uncertain delayed multi-agent systems with Markovian switching are considered. It is shown that the robust synchronisation of such an uncertain multi-agent network could be achieved by a protocol that each controller being partially delay-dependent or disordering could robustly stabilise a given single Markovian jump system. As for these cases, the proposed protocols could be obtained by solving certain algebraic Riccati equations and inequalities, which also involve weighting factors and depend on the eigenvalues of the Laplacian graph.
Acknowledgments
The authors would like to thank the associate editor and the reviewers for their very helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China under Grants 61104066, 61374043 and 61473140, the China Postdoctoral Science Foundation funded project under Grant 2012M521086, the Program for Liaoning Excellent Talents in University under Grant LJQ2013040, the Natural Science Foundation of Liaoning Province under Grant 2014020106.
Disclosure statement
No potential conflict of interest was reported by the authors.
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Notes on contributors
Guoliang Wang
Guoliang Wang received the B.Sc., M.Sc. and Ph.D. degrees in control theory and engineering from the Northeastern University of Shenyang, China, in 2004, 2007 and 2010, respectively. He is presently an associate professor in the school of information and control engineering, Liaoning Shihua University, Fushun, Liaoning, China. He has authored/co-authored over 40 publications. His research interests include Markovian jump systems, singular systems, stochastic control and filtering.
Qingling Zhang
Qingling Zhang received the B.S. and M.S. degrees from the Mathematics Department and the Ph.D. degree from the Automatic Control Department of Northeastern University, Shenyang, China, in 1982, 1986, and 1995, respectively. Since 1997, he has been a Professor with Northeastern University. He is also a member of the University Teaching Advisory Committee of National Ministry of Education. He has published six books and more than 230 papers about control theory and applications.
Chunyu Yang
Chunyu Yang received the B.Sc., M.Sc. and Ph.D. degrees in control theory and engineering from the Northeastern University of Shenyang, China, in 2002, 2004 and 2009, respectively. He is presently an associate professor in the school of information and electrical engineering, China University of Mining and Technology, Xuzhou, China. His research interests include descriptor systems, singular perturbed systems, and electrical systems.