Partial state estimation of LTI systems with multiple constant time-delays

Mohajerpoor, Reza, Abdi, Hamid, Shanmugam, Lakshmanan and Nahavandi, Saeid 2016, Partial state estimation of LTI systems with multiple constant time-delays, Journal of the Franklin Institute, vol. 353, no. 2, pp. 541-560, doi: 10.1016/j.jfranklin.2015.11.011.

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Title Partial state estimation of LTI systems with multiple constant time-delays
Author(s) Mohajerpoor, Reza
Abdi, HamidORCID iD for Abdi, Hamid
Shanmugam, LakshmananORCID iD for Shanmugam, Lakshmanan
Nahavandi, SaeidORCID iD for Nahavandi, Saeid
Journal name Journal of the Franklin Institute
Volume number 353
Issue number 2
Start page 541
End page 560
Total pages 20
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2016-01
ISSN 0016-0032
Keyword(s) Science & Technology
Physical Sciences
Automation & Control Systems
Engineering, Multidisciplinary
Engineering, Electrical & Electronic
Mathematics, Interdisciplinary Applications
Summary Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 - delay-dependent, and 2 - internal-delay independent. The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen's inequality, and improved Park's inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.
Language eng
DOI 10.1016/j.jfranklin.2015.11.011
Field of Research 090602 Control Systems, Robotics and Automation
0102 Applied Mathematics
0906 Electrical And Electronic Engineering
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2016, Elsevier
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