Partial eigenvalue assignment  with time delayrobustness

Xiaobin Mao; Hua Dai

doi:10.3934/naco.2013.3.207

Article Contents

2013, Volume 3, Issue 2: 207-221. Doi: 10.3934/naco.2013.3.207

This issue Previous Article A two-phase method for multidimensional number partitioning problem Next Article Subspace trust-region algorithm with conic model for unconstrained optimization

Partial eigenvalue assignment with time delay robustness

Xiaobin Mao^1, and
Hua Dai^1,

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

Received: November 30, 2011

Revised: December 31, 2012

Published: March 2013

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 93B55, 93B52; Secondary: 65F18, 15A29.

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