Asymptotic properties of zero dynamics for nonlinear discretized systems with time delay via Taylor method

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• 作者：Cheng Zeng (1) (2)
  Shan Liang (2)
  Hongbing Li (3)
  
  1. College of Science ; Guizhou Institute of Technology ; Guiyang ; 550003 ; Guizhou ; China
  2. College of Automation ; Chongqing University ; Chongqing ; 400044 ; China
  3. College of Computer Science and Engineering ; Chongqing Three Gorges University ; Chongqing ; 404000 ; China
  
• 关键词：Nonlinear sampled ; data model ; Zero dynamics ; Zero ; order hold ; Time discretization ; Taylor method ; Time delay ; Stability properties
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：79
• 期：2
• 页码：1481-1493
• 全文大小：252 KB
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• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

Most real world plants often operate in continuous-time case and involve time delay. These models are typically described by ordinary differential equations. However, to utilize and analyze these data, the control signals must first be discretized. In this paper, a new discretization method for obtaining an approximate sampled-data model of a nonlinear continuous-time system with time delay is proposed. The presented approach is based on the Taylor method and zero-order hold assumption, which can be used to approximate the system output and its derivatives in such a way as to obtain a local truncation error between the output of the resulting sampled-data model and true continuous-time system output. More importantly, on the basis of this discretized representation, we explicitly derive the mathematical structure of nonlinear discrete-time zero dynamics in the case of time delay. The main contribution is to analyze the stability of sampling zero dynamics for the proposed model with time delay. The ideas presented here generalize the well-known results from the linear system to nonlinear case.