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Abstract and Applied Analysis
Volume 2014, Article ID 817534, 12 pages
Research Article

Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay

1College of Automation, Chongqing University, Chongqing 400044, China
2College of Science, Guizhou Institute of Technology, Guiyang, Guizhou 550003, China

Received 24 March 2014; Revised 20 July 2014; Accepted 29 July 2014; Published 28 August 2014

Academic Editor: Jaeyoung Chung

Copyright © 2014 Cheng Zeng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous-time systems with time delay and relative degree two. This paper analyzes the asymptotic behavior of zero dynamics for the sampled-data models corresponding to the continuous-time systems mentioned above, and further gives an approximate expression of the zero dynamics in the form of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zero dynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideas presented here generalize well-known results from the delay-free control system to time-delay case.