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Two New Finite-time Convergence Criterions and Application to Solve Time Varying Sylvester Equation and Pseudo-inverse of a Matrix

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Abstract

Based on the second order differential equation, this paper investigates finite-time stability, finite-time convergence criterions and estimates of convergence time. The main contributions of this paper lie in the fact that two new finite-time convergence criterions are proposed through the property of the second order differential equation and their upper bound of the convergence time is derived. In addition, our finite-time stability criterions are used to a recurrent neural network for solving time-varying Sylvester equation and Pseudo-Inverse of a Matrix. At last, a numerical example and a Pseudo-Inverse of a Matrix demonstrate the effectiveness of our method.

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Author information

Authors and Affiliations

  1. Department of Basic Courses, Zhengzhou University of Science & Technology, Zhengzhou, Hennan, 450064, China

    Peng Miao

  2. School of Civil Engineering and Architecture, Zhengzhou University of Science & Technology, Zhengzhou, Hennan, 450064, China

    Liujun Fan

  3. School of Economics and Trade, Xinhua College of Sun Yat-sen University (Dongguan), Guangzhou, 523133, China

    Daoyuan Zhang

Authors
  1. Peng Miao
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  2. Liujun Fan
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  3. Daoyuan Zhang
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Corresponding author

Correspondence to Peng Miao.

Additional information

Recommended by Associate Editor Yueying Wang under the direction of Editor Hamid Reza Karimi.

This work was supported by the Key Scientific Research Foundation of Education Bureau of Henan Province, China (Grant No. 20B110020, 21B110008) and the Key scientific and technological projects in the field of high and new technology in Henan Province, China (Grant No. 172102210113).

Peng Miao received his B.S. degree from the Department of Mathematics at the Normal University of Nanyang of China, in 2012, an M.Sc. degree from the College of Science at China Three Gorges University, in 2015. Now, he is a lecturer in Department of Basic Courses, Zhengzhou University of Science & Technology. His research interests include nonlinear systems, nonlinear control, adaptive control and neural networks.

Liujun Fan received his B.S. degree from the School of Civil Engineering and Communication at the North China University of Water Resources and Electric Power, in 2012, an M.Sc. degree from the College of Civil Engineering and Architecture at China Three Gorges University, in 2015. Now, he is a lecturer in the School of Civil Engineering and Architecture, Zhengzhou University of Science & Technology. His research interests include soil mechanics, landslide prediction and antiskid and optimization of building structure.

Daoyuan Zhang received his B.S. and M.Sc. degrees in applied mathematics from China Three Gorges University, Yichang, China, in 2012 and 2015, respectively. He studied at University of Pretoria from 2016 to 2017, Pretoria, South Africa. Now he is a lecturer in Xinhua College of Sun Yat-Sen University. His research interests include networked control systems, sampled-data control, energy efficiency.

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Miao, P., Fan, L. & Zhang, D. Two New Finite-time Convergence Criterions and Application to Solve Time Varying Sylvester Equation and Pseudo-inverse of a Matrix. Int. J. Control Autom. Syst. 19, 1570–1577 (2021). https://doi.org/10.1007/s12555-019-1043-z

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  • DOI: https://doi.org/10.1007/s12555-019-1043-z

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