Exponential admissibility analysis for singular systems with time-varying delay based on a parameter-dependent reciprocally convex inequality

Abstract

This paper is concerned with the exponential admissibility problem of singular systems with interval time-varying delay. A parameter-dependent reciprocally convex inequality (PDRCI) is developed, which covers some existing ones as its special case. By using the system decomposition method, the considered system is decomposed into differential equations and algebraic ones. Unlike some existing works, the components of state vectors of the subsystems are applied to construct a new augmented Lyapunov–Krasovkii functional (LKF) with fewer decision variables. Based on the new integral inequality and augmented LKF, two exponential admissibility criteria are obtained in terms of linear matrix inequalities (LMIs). It should be mentioned that the derivative of the time-varying delay does not need to be smaller than one in this paper. The effectiveness of the proposed methods is demonstrated by two examples.

Keywords:

• Singular systems
• interval time-varying delay
• system decomposition method
• parameter-dependent reciprocally convex inequality

Acknowledgements

The authors would like to thank the editors and the referees for carefully reading the paper and for their comments which have helped to greatly improve the paper.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61973070], the Liaoning Revitalization Talents Program [grant number XLYC1802010], and in part by SAPI Fundamental Research Funds [grant number 2018ZCX22].

Notes on contributors

Yufeng Tian

Yufeng Tian received the B.Sc. degree in Mathematics from North eastern University, Shen Yang, China, in 2016, the M.Sc degree in System theory from North eastern University, Shen Yang, China, in 2018.He is now pursuing the Ph.D. degree in Control theory and control engineering from North eastern University, Shenyang, China. His research interests include neural networks, fuzzy system, Markov jump system, stability analysis, control and filtering design.

Zhanshan Wang

Zhanshan Wang (M'09-SM'17) received the M.S. degree in control theory and control engineering from Liaoning Shihua University, Fushun, China, in 2001, and the Ph.D. degree in control theory and control engineering from North eastern University, Shenyang, China, in 2006. He has been a professor in North eastern University since 2010. He has authored or co-authored over 100 journal and conference papers and five monographs. He holds ten patents. His current research interests include the stability analysis of recurrent neural networks, fault diagnosis, fault tolerant control, intelligent automation and their applications in power systems and smart grid. Dr. Wang was an Associate Editor of the IEEE Transactions on Neural Networks and Learning Systems. He is an Associate Editor of Acta Automatica Sinica.