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2012 (Vol. 4, Issue: 18)
Article Information:

Stabilization of State-derivative Feedback Control with Time Delay

Witchupong Wiboonjaroen and Sarawut Sujitjorn
Corresponding Author:  Sarawut Sujitjorn 

Key words:  Delay differential equation, eigenvalue assignment, feedback controller, lambert W function, neutral system, state-derivative feed back,
Vol. 4 , (18): 3201-3208
Submitted Accepted Published
December 23, 2011 January 21, 2012 September 15, 2012
Abstract:

This study considers the problem of state-derivative feedback controller design via eigenvalue assignment for LTI systems of linear Delay Differential Equations (DDEs) with a single delay. Unlike simple LTI systems, the systems described by DDEs have an infinite eigenspectrum and it is not feasible to assign all closed-loop eigenvalues. The paper proposes a method to assign a critical subset of them using an approach of the matrix Lambert W function. The solution has an analytical form expressed in terms of the parameters of the DDE. With the proposed method, one can extend a conventional eigenvalue assignment method for a feedback controller to a delayed LTI system. A scheme including filtered state-derivative feedback is proposed to overcome the destabilizing effect of feedback delays. Proofs of the proposed method and numerical examples are presented.
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  Cite this Reference:
Witchupong Wiboonjaroen and Sarawut Sujitjorn, 2012. Stabilization of State-derivative Feedback Control with Time Delay.  Research Journal of Applied Sciences, Engineering and Technology, 4(18): 3201-3208.
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ISSN (Online):  2040-7467
ISSN (Print):   2040-7459
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