Robust stochastic stability of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises

Abstract

In this paper, the robust stochastic stability is investigated for a class of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises. Using the method of stochastic Lyapunov functionals construction, it is shown that impulses can stabilise the original impulse-free unstable systems. Moreover, the stability property of the impulse-free systems can be retained in the cases of appropriately large impulsive time interval. Some numerical examples are exploited to demonstrate the effectiveness and the superiority of the proposed results.

Keywords:

• impulse
• delay
• robust stochastic stability
• Markovian jump parameter

Acknowledgements

The authors would like to thank the associate editor and the anonymous reviewers for their constructive comments and suggestions that improved the quality of the paper.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 60904027], [grant number 11101311]; ‘the Fundamental Research Funds for the Central Universities’ and the Shanghai Committee of Science and Technology [grant number 13ZR1444500].

Notes on contributors

Yu Zhang

Yu Zhang received her BSc degree from the Department of Applied Mathematics, Northeastern University, Shenyang, China, in 2002, and the PhD degree from the Department of Mathematics, Tongji University, Shanghai, China, in 2007, respectively. She was a Research Assistant at the City University of Hong Kong, Hong Kong, China, from July 2005 to October 2005. Since July 2007, she has been with the Department of Mathematics, Tongji University, Shanghai, China. She is currently an Associate Professor at Tongji University. She is the author or coauthor of more than 20 research articles. Her research interests include stability theory, discrete-time stochastic systems and impulsive control systems.

Cheng Wang

Cheng Wang received his MS degree in Computational Mathematics and PhD degree in Applied Mathematics from Tongji University in 2004 and 2007, respectively. Since July 2007, he has been with the Department of Mathematics at Tongji University. His primary research interest lies at the interface of applied mathematics and computational science. His research includes the development of stable and efficient numerical methods for large-scale systems of differential equations with applications to the modelling and simulation in engineering.