2010
DOI: 10.1177/1077546309341102
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Eigenvalue Assignment via the Lambert W Function for Control of Time-delay Systems

Abstract: In this paper, we consider the problem of feedback controller design via eigenvalue assignment for linear time-invariant systems of linear delay differential equations (DDEs) with a single delay. Unlike ordinary differential equations (ODEs), DDEs have an infinite eigenspectrum, and it is not feasible to assign all closed-loop eigenvalues. However, we can assign a critical subset of them using a solution to linear systems of DDEs in terms of the matrix Lambert W function. The solution has an analytical form ex… Show more

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Cited by 63 publications
(49 citation statements)
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“…In [29], a numerical stabilization method was developed to obtain the rightmost eigenvalues and move them to the left half plane (LHP) using sensitivities with respect to changes in the control gain. This approach has been compared to the Lambert W function-based approach in [15]. The approach can be applied to design observers [25].…”
Section: Description Of Approach Referencesmentioning
confidence: 99%
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“…In [29], a numerical stabilization method was developed to obtain the rightmost eigenvalues and move them to the left half plane (LHP) using sensitivities with respect to changes in the control gain. This approach has been compared to the Lambert W function-based approach in [15]. The approach can be applied to design observers [25].…”
Section: Description Of Approach Referencesmentioning
confidence: 99%
“…one can stabilize, improve performance, and/or meet time-domain specifications for the system (1) (e.g., see [15,22]), under the assumption that all the state variables, xðtÞ, can be measured directly. This is achieved by choosing K and K d ð2 R rÂn Þ based on desired rightmost closed-loop eigenvalues.…”
Section: Description Of Approach Referencesmentioning
confidence: 99%
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“…One can choose feedback gains to assign the rightmost pole of systems with time-delays to desired positions in the complex plane based on the Lambert W function approach (Yi et al, 2010b). Consider a simple, but unstable, example given byẋ…”
Section: C1 Limits In Assignment Of Eigenvaluesmentioning
confidence: 99%
“…The Lambert W function-based approach provides a method for design of feedback controllers via pole placement (Yi et al, 2010b …”
Section: C1 Limits In Assignment Of Eigenvaluesmentioning
confidence: 99%