# American Institute of Mathematical Sciences

2013, 3(2): 207-221. doi: 10.3934/naco.2013.3.207

## Partial eigenvalue assignment with time delay robustness

 1 Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China, China

Received  December 2011 Revised  January 2013 Published  April 2013

The partial eigenvalue assignment problem concerns reassigning a few of undesired eigenvalues of a linear system to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). This paper considers the partial eigenvalue assignment problem with time delay robustness. A time delay robustness measure is presented by analyzing the sensitivity of the assigned eigenvalues with respect to time delay. The problem is formulated as an unconstrained minimization problem with the cost function involving the time delay robustness measure. A numerical algorithm with analytical formulation of the gradient for the cost function is provided. A numerical example is included to show the effectiveness of the proposed method.
Citation: Xiaobin Mao, Hua Dai. Partial eigenvalue assignment with time delay robustness. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 207-221. doi: 10.3934/naco.2013.3.207
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