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Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling

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  • Control Theory and Applications
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Abstract

It is well-known that existence of unstable sampling zeros is recognized as a major barrier in many control problems, and stability of sampling zeros, in general, depends on the type of hold circuit used to generate the continuous-time system input. This paper is concerned with stability of limiting zeros, as the sampling period tends to zero, of multivariable sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time plant with the relative degrees being two and three, and a sampler in cascade. In particular, the main focus of the paper is how to preserve the stability of limiting zeros when at least one of the relative degrees of a multivariable system is more than two. In this case, the asymptotic properties of the limiting zeros on the basis of normal form representation of continuous-time systems are analyzed and approximate expressions for their stability are discussed as power series expansions with respect to a sufficiently small sampling period. More importantly, unstable sampling zeros of the sampled-data models mentioned above can be avoided successfully through the contribution of this paper, whereas a zero-order hold (ZOH) or a fractional-order hold (FROH) fails to do so. It is a further extension of previous results for single-input single-output cases to multivariable systems.

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Author information

Authors and Affiliations

  1. College of Computer Science & Technology, Guizhou University, Guiyang Guizhou, 550025, China

    Cheng Zeng & Shuwen Xiang

  2. School of Science, Guizhou Institute of Technology, Guiyang Guizhou, 550003, China

    Cheng Zeng

  3. College of Automation, Chongqing University, Chongqing, 400044, China

    Shan Liang

Authors
  1. Cheng Zeng
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  2. Shan Liang
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  3. Shuwen Xiang
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Corresponding authors

Correspondence to Cheng Zeng or Shuwen Xiang.

Additional information

Recommended by Associate Editor Juhoon Back under the direction of Editor Myo Taeg Lim. This work is supported by the National Natural Science Foundation of China (61763004) and the Joint Funds of the Natural Science Foundation Project of Guizhou (Grant No. LH[2014]7362). The authors also gratefully acknowledge the helpful comments and suggestions of the viewers, which have improved the presentation.

Cheng Zeng received his Bachelor of Science degree in mathematics and applied mathematics from Sichuan Normal University, China, and his Master of Science degree in basic mathematics from Guizhou University, China, in 2003 and 2008, respectively. In 2014, He received his Ph.D. degree in control theory and control engineering at the University of Chongqing, China. Since 2014, he received the professional title and has been working in the Guizhou Institute of Technology. From 2014 to 2018, he has been working toward the postdoctoral work in computer science and technology in Guizhou University, China. His research areas include discrete-time and sampled-data systems, nonlinear stochastic model, adaptive differential game and control.

Shan Liang received an Master of Science degree in control science and engineering from the College of Automation of the University of Chongqing in 1995, and in 2004, he obtained a Ph.D. degree from the Department of Mechanical Systems Engineering of Kumamoto University, Japan. Since 2000, his research interest covers nonlinear systems, adaptive control and sensor network.

Shuwen Xiang received his B.Sc., B.E., and Ph.D. degrees from South Central University for Nationalities, Sichuan University, and Zhejiang University, China, in 1986, 1989, and 1998, respectively. He is currently a Professor of Mathematics and Computer Science, in Guizhou University. His research areas include nonlinear analysis, game theory, discretized models.

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Zeng, C., Liang, S. & Xiang, S. Improving the Stability Behavior of Limiting Zeros for Multivariable Systems Based on Multirate Sampling. Int. J. Control Autom. Syst. 16, 2621–2633 (2018). https://doi.org/10.1007/s12555-017-0693-y

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  • DOI: https://doi.org/10.1007/s12555-017-0693-y

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