CALCULATION OF THE STRUCTURED SINGULAR-VALUE WITH GRADIENT-BASED OPTIMIZATION ALGORITHMS ON A LIE GROUP OF STRUCTURED UNITARY MATRICES

Authors
DEHAENE J YI C DEMOOR B
Citation
J. Dehaene et al., CALCULATION OF THE STRUCTURED SINGULAR-VALUE WITH GRADIENT-BASED OPTIMIZATION ALGORITHMS ON A LIE GROUP OF STRUCTURED UNITARY MATRICES, IEEE transactions on automatic control, 42(11), 1997, pp. 1596-1600
Citations number
12
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control","Engineering, Eletrical & Electronic
Journal title
IEEE transactions on automatic control → ACNP
ISSN journal
00189286
Volume
42
Issue
11
Year of publication
1997
Pages
1596 - 1600
Database
ISI
SICI code
0018-9286(1997)42:11<1596:COTSSW>2.0.ZU;2-M
Abstract
The structured singular value problem, which is a basic problem in rob ustness analysis and design of multivariable controllers, can be formu lated as an optimization problem over the manifold of unitary matrices with a given structure. We show how geometric optimization methods, s uch as the steepest ascent method and the conjugate gradient method fo r optimization on a Riemannian manifold, lead to algorithms giving a g uaranteed nontrivial lower bound for thr structured singular value.