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Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities

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  • Control Theory and Applications
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Abstract

This paper is concerned with the stability analysis of linear discrete time-delay systems. New discrete inequalities for single summation and double summation are presented to estimate summation terms in the forward difference of Lyapunov-Krasovskii functional (LKF), which are more general than some commonly used summation inequalities. Through the construction of an augmented LKF, improved delay-dependent stability criteria for discrete time-delay systems are established. Based on this, a time-delayed controller is derived for linear discrete time-delay systems. Finally, the advantages of the proposed criteria are revealed from the solutions of the numerical examples.

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Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, Hunan, 412007, P. R. China

    Shenping Xiao & Hong-Bing Zeng

  2. Key Laboratory for Electric Drive Control and Intelligent Equipment of Hunan Province, Zhuzhou, Hunan, 412007, P. R. China

    Shenping Xiao & Hong-Bing Zeng

  3. School of Information Science and Engineering, Northeastern University, Shenyang, Liaoning, 110004, P. R. China

    Linxing Xu

  4. Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Kok Lay Teo

  5. Department of Mathemtics and Statsitics, Curtin University, Perth, WA, 6102, Australia

    Kok Lay Teo

Authors
  1. Shenping Xiao
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  2. Linxing Xu
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  3. Hong-Bing Zeng
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  4. Kok Lay Teo
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Corresponding author

Correspondence to Shenping Xiao.

Additional information

Recommended by Associate Editor Young Ik Son under the direction of Editor PooGyeon Park. This work was supported by the National Nature Science Foundation of China (Grant Nos. 61672225, 61741308), the Natural Science Foundation of Hunan Province of China (Grant No. 2015JJ5021).

Shen-Ping Xiao received the B.S. degree in automation from Northeastern University, Shenyang, China, in 1988, M.S. degree in computer science from Central South University of Forestry, Changsha, China, in 2002, and Ph.D. degree in control theory and control engineering from Central South University, Changsha, China, in 2008. He has been with the Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, China, where he is currently a professor of automatic control engineering. Currently, he is working as a research fellow in the Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia. His current research interests are time-delay systems, networked control systems and power and energy systems.

Lin-Xing Xu received the B.S. degree in electrical engineering and automation from Nanjing University of Science and Technology ZiJin College, Nanjing, China, in 2009, his M.S. degree in control theory and control engineering from Hunan University of Technology, Zhuzhou, China, in 2013. Currently, he is pursuing the Ph.D. degree in control theory and control engineering from Northeastern University, Shenyang, China. His research interests are time-delay systems, fault-tolerant control and multi-agent coordination.

Hong-Bing Zeng received his B.S. degree in electrical engineering from Tianjin University of Technology and Education, Tianjin, China, in 2003, an M.S. degree in computer science from Central South University of Forestry, Changsha, China in 2006, and a Ph.D. degree in control science and engineering from Central South University, Changsha, China, in 2012, respectively. From September 2013 to August 2014, he was working as a Postdoctoral Research Associate in the Department of Electrical Engineering, Yeungnam University, Kyongsan, Korea. From March 2016 to February 2017, he was a Research Fellow in the Department of Mathematics and Statistics, Curtin University, Perth, WA, Australia. Currently, he is working as a Professor in the Department of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, China. His research interests are time-delay systems, neural networks and networked control systems.

Kok Lay Teo received his Ph.D. degrees in electrical engineering from the University of Ottawa, Canada. He was with the Department of Applied Mathematics, University of New SouthWales, Australia, the Department of Industrial and Systems Engineering, National University of Singapore, Singapore, the Department of Mathematics, the University of Western Australia, Australia. In 1996, he joined the Department of Mathematics and Statistics, Curtin University of Technology, Australia, as Professor. He then took up the position of Chair Professor of Applied Mathematics and Head of Department of Applied Mathematics at the Hong Kong Polytechnic University, China, from 1999 to 2004. He returned to Curtin University as Professor and Head of the Department of Mathematics and Statistics from 2015 to 2010. He has been John Curtin Distinguished Professor at Curtin University since 2011. He was a member of the ARC’s Mathematical, Information, and Computing Sciences Research Evaluation Committee for ERA 2010 and ERA2015. He published 5 books and over 500 journal papers. He has a software package, MISER3.3, for solving general constrained optimal control problems. His editorial positions include serving as Editor-in-Chief of the Journal of Industrial and Management Optimization; Numerical Algebra, Control and Optimization; and Cogent Mathematics, and as a member of editorial board of a number of journals such as Automatica, Journal of Global Optimization, Journal of Optimization Theory and Applications, Optimization and Engineering, Discrete and Continuous Dynamic Systems, Optimization Letters, and Applied Mathematical Modelling. His research interests include both the theoretical and practical aspects of optimal control and optimization, and their practical applications such as in signal processing in telecommunications, and financial portfolio optimization.

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Xiao, S., Xu, L., Zeng, HB. et al. Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities. Int. J. Control Autom. Syst. 16, 1592–1602 (2018). https://doi.org/10.1007/s12555-017-0279-8

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  • DOI: https://doi.org/10.1007/s12555-017-0279-8

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