An approach to eigenvalue assignment for systems of linear time-invariant (LTI) delay differential equations (DDEs), based upon the solution in terms of the matrix Lambert W function, is applied to the problem of robust control design for perturbed LTI systems of DDEs, and to the problem of time-domain response specifications. Robust stability of the closed-loop system can be achieved through eigenvalue assignment combined with the real stability radius concept. For a LTI system of DDEs with a single delay, which has an infinite number of eigenvalues, the recently developed Lambert W function-based approach is used to assign a dominant subset of them, which has not been previously feasible. Also, an approach to time-domain specifications for the transient response of systems of DDEs is developed in a way similar to systems of ordinary differential equations using the Lambert W function-based approach.
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e-mail: syjo@umich.edu
e-mail: pwn@umich.edu
e-mail: ulsoy@umich.edu
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Robust Control and Time-Domain Specifications for Systems of Delay Differential Equations via Eigenvalue Assignment
Sun Yi,
Sun Yi
Department of Mechanical Engineering,
e-mail: syjo@umich.edu
University of Michigan
, 2350 Hayward Street, Ann Arbor, MI 48109-2125
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Patrick W. Nelson,
Patrick W. Nelson
Center for Computational Medicine and Biology,
e-mail: pwn@umich.edu
University of Michigan
, 100 Washtenaw Avenue, Ann Arbor, MI 48109-2218
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A. Galip Ulsoy
A. Galip Ulsoy
Department of Mechanical Engineering,
e-mail: ulsoy@umich.edu
University of Michigan
, 2350 Hayward Street, Ann Arbor, MI 48109-2125
Search for other works by this author on:
Sun Yi
Department of Mechanical Engineering,
University of Michigan
, 2350 Hayward Street, Ann Arbor, MI 48109-2125e-mail: syjo@umich.edu
Patrick W. Nelson
Center for Computational Medicine and Biology,
University of Michigan
, 100 Washtenaw Avenue, Ann Arbor, MI 48109-2218e-mail: pwn@umich.edu
A. Galip Ulsoy
Department of Mechanical Engineering,
University of Michigan
, 2350 Hayward Street, Ann Arbor, MI 48109-2125e-mail: ulsoy@umich.edu
J. Dyn. Sys., Meas., Control. May 2010, 132(3): 031003 (7 pages)
Published Online: April 14, 2010
Article history
Received:
July 1, 2008
Revised:
February 12, 2010
Online:
April 14, 2010
Published:
April 14, 2010
Citation
Yi, S., Nelson, P. W., and Ulsoy, A. G. (April 14, 2010). "Robust Control and Time-Domain Specifications for Systems of Delay Differential Equations via Eigenvalue Assignment." ASME. J. Dyn. Sys., Meas., Control. May 2010; 132(3): 031003. https://doi.org/10.1115/1.4001339
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