New state transformations of time-delay systems with multiple delays and their applications to state observer design

Huong, D.C. and Trinh, H. 2016, New state transformations of time-delay systems with multiple delays and their applications to state observer design, Journal of the Franklin Institute, vol. 353, no. 14, pp. 3487-3523, doi: 10.1016/j.jfranklin.2016.06.033.

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Title New state transformations of time-delay systems with multiple delays and their applications to state observer design
Author(s) Huong, D.C.
Trinh, H.ORCID iD for Trinh, H.
Journal name Journal of the Franklin Institute
Volume number 353
Issue number 14
Start page 3487
End page 3523
Total pages 37
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2016-09
ISSN 0016-0032
Keyword(s) Science & Technology
Physical Sciences
Automation & Control Systems
Engineering, Multidisciplinary
Engineering, Electrical & Electronic
Mathematics, Interdisciplinary Applications
Summary This paper addresses the problem on how to systematically compute state transformations of a general class of time-delay systems with multiple time delays in the state and output vectors, and applications of these state transformations to state observer design. First, a forward state transformation problem is studied. For this, we present a two-stage coordinate transformation method to transform any given time-delay system into an observable canonical form where time delays appear in the input and output vectors, but not in the state vector. The significance of such a coordinate transformation is that a Luenberger-type state observer can be easily designed in the new coordinate system. Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system. Therefore, by using both the forward and the backward state transformations, state observers for time-delay systems can be systematically designed. Our approach based on the new state transformations enables the design of state observers of a more general class of time-delay systems than existing works in the literature. Conditions for the existence of the state transformations and an algorithm for computing them are provided in this paper. Numerical examples and simulation results are given to illustrate the effectiveness of our proposed design method.
Language eng
DOI 10.1016/j.jfranklin.2016.06.033
Field of Research 010203 Calculus of Variations, Systems Theory and Control Theory
010204 Dynamical Systems in Applications
090602 Control Systems, Robotics and Automation
Socio Economic Objective 970109 Expanding Knowledge in Engineering
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Grant ID DP130101532
Copyright notice ©2016, The Franklin Institute
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