Open Access
2014 Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay
Cheng Zeng, Shan Liang, Jiaqi Zhong, Yingying Su
Abstr. Appl. Anal. 2014: 1-12 (2014). DOI: 10.1155/2014/817534


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.


Download Citation

Cheng Zeng. Shan Liang. Jiaqi Zhong. Yingying Su. "Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay." Abstr. Appl. Anal. 2014 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023135
MathSciNet: MR3256262
Digital Object Identifier: 10.1155/2014/817534

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top