Geodesic
On computing stabilizability radii of linear time-invariant continuous systems
Electronic transactions on numerical analysis, Tome 40 (2013), pp. 407-413
In this paper we focus on a non-convex and non-smooth singular value optimization problem. Our framework encompasses the distance to stabilizability of a linear system $(A,B)$ when both $A$ and $B$ or only one of them are perturbed. We propose a trisection algorithm for the numerical solution of the singular value optimization problem. This method requires $O(n^4)$ operations on average, where $n$ is the order of the system. Numerical experiments indicate that the method is reliable in practice.
Classification : 65F15, 93D15, 65K10
Keywords: stabilizability radius, optimization, trisection algorithm, linear time-invariant continuous system 
@article{ETNA_2013__40__a4,
     author = {Khanh,  D.C. and Quyen,  H.T. and Thanh,  D.D.X.},
     title = {On computing stabilizability radii of linear time-invariant continuous systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {407--413},
     year = {2013},
     volume = {40},
     zbl = {1287.93067},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2013__40__a4/}
}
TY  - JOUR
AU  - Khanh,  D.C.
AU  - Quyen,  H.T.
AU  - Thanh,  D.D.X.
TI  - On computing stabilizability radii of linear time-invariant continuous systems
JO  - Electronic transactions on numerical analysis
PY  - 2013
SP  - 407
EP  - 413
VL  - 40
UR  - http://geodesic.mathdoc.fr/item/ETNA_2013__40__a4/
LA  - en
ID  - ETNA_2013__40__a4
ER  - 
%0 Journal Article
%A Khanh,  D.C.
%A Quyen,  H.T.
%A Thanh,  D.D.X.
%T On computing stabilizability radii of linear time-invariant continuous systems
%J Electronic transactions on numerical analysis
%D 2013
%P 407-413
%V 40
%U http://geodesic.mathdoc.fr/item/ETNA_2013__40__a4/
%G en
%F ETNA_2013__40__a4
Khanh,  D.C.; Quyen,  H.T.; Thanh,  D.D.X. On computing stabilizability radii of linear time-invariant continuous systems. Electronic transactions on numerical analysis, Tome 40 (2013), pp. 407-413. http://geodesic.mathdoc.fr/item/ETNA_2013__40__a4/