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Time discretization of nonlinear time-delay system using matrix exponential method

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Abstract

A time discretization method for nonlinear time-delay systems is proposed in this paper. The proposed method is based on the matrix exponential method and includes the automatic correction of rounding errors. It is robust to ill-conditioned problems and suitable for any nonlinear system. In the proposed algorithm, each sampling time interval is divided into two subintervals to be considered separately according to the time delay and the sampling period. The performance of the proposed discretization procedure is evaluated by two case studies.

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Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Xian Jiaotong University, Xian, China

    Zheng Zhang

  2. Key Laboratory of Ministry of Education for Special Area Highway Engineering and the Key Laboratory of Ministry of Education for Road Construction Technology and Equipment, Xian, China

    Zheng Zhang

  3. Mechanical Engineering at Huaihai Institute of Technology, Lianyungang, China

    Yuanliang Zhang

  4. EE of Jeon Buk National University, Jeonju, Korea

    Young Won Chang

  5. School of Electronics Engineering, Jeon Buk National University, Jeonju, Korea

    Kil To Chong

Authors
  1. Zheng Zhang
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  2. Yuanliang Zhang
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  3. Young Won Chang
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  4. Kil To Chong
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Corresponding author

Correspondence to Kil To Chong.

Additional information

Recommended by Editor Young Il Lee.

This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (No. 20110004905) and BK21 of Jeonbuk National University, and partially supported by the Fundamental Research Funds for the Central University of China (xjj2011072, CHD2011SY004, CHD2011SY002).

Zheng Zhang received his Ph.D. degree in Mechanical Engineering from Xi’an Jiaotong University, in 2005. He is currently a lecturer at the School of Mechanical Engineering, Xi’an Jiaotong University, China. He is also a researcher of the Key Laboratory of Ministry of Education for Special Area Highway Engineering and the Key Laboratory of Ministry of Education for Road Construction Technology and Equipment in Chang’an University, Xian, China. His research interests are in the areas of nonlinear systems control, electric vehicle and time-delay systems.

Yuanliang Zhang received his Ph.D. degree in Electronics Engineering from Chonbuk National University, in 2009. Currently, he is a lecturer at the School of Mechanical Engineering, Huaihai Institute of Technology, Lianyungang, China. His research interests are in the areas of nonlinear systems control, time-delay systems, and neural networks.

Young Won Chang received his Ph.D. degree in Computer Engineering from Chonbuk National University, Jeonju, Korea, in 2010. Currently, he is an Adjunct Professor at Brain Korea21, Chonbuk National University, Jeonju, Korea. His research interests are in the areas of robotics, software engineering, vision processing, and system testing.

Kil To Chong received his Ph.D. degree in Mechanical Engineering from Texas A&M University, College Station, in 1995. Currently, he is a Professor at the School of Electronics and Information Engineering, Chonbuk National University, Jeonju, Korea, and Head of the Mechatronics Research Center granted from the Korea Science Foundation. His research interests are in the areas of motor fault detection, network system control, time-delay systems, and neural networks.

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Zhang, Z., Zhang, Y., Chang, Y.W. et al. Time discretization of nonlinear time-delay system using matrix exponential method. Int. J. Control Autom. Syst. 9, 1219–1226 (2011). https://doi.org/10.1007/s12555-011-0624-2

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  • DOI: https://doi.org/10.1007/s12555-011-0624-2

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