Title :
Summary of recent results on the decay rate of the Hankel singular values
Author_Institution :
Dept. of Electr. & Comput. Eng., Rice Univ., Houston, TX, USA
Abstract :
The purpose of the paper is to investigate the issue of the decay rate of the Hankel singular values of a linear system. This issue is of considerable interest in model reduction, by means of balanced truncation for instance, since the sum of the neglected singular values provides an upper bound for an appropriate norm of the approximation error. The decay rate involves a new set of invariants associated with a linear system, which are obtained by evaluating a modified transfer function at the poles of the system
Keywords :
Lyapunov methods; eigenvalues and eigenfunctions; linear systems; matrix algebra; multidimensional systems; poles and zeros; reduced order systems; transfer functions; Cauchy matrix; Hankel operator; Hankel singular values; Lvapunov equations; approximation error; balanced truncation; decay rate; finite-dimensional time-invariant system; linear system; majorization; model reduction; modified transfer function; neglected singular values; poles; upper bound; Approximation error; Ear; Eigenvalues and eigenfunctions; Equations; Large-scale systems; Linear systems; Reduced order systems; Transfer functions; Uniform resource locators; Upper bound;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980428
