Realization theory for two-time-scale distributions

Author

Oloomi, Hossein ; Shafai, Bahram

Author_Institution

Dept. of Electr. Eng., Purdue Univ., Fort Wayne, IN, USA

Volume

5

fYear

2003

fDate

4-6 June 2003

Firstpage

4476

Abstract

In this paper we investigate the problem of approximating the Markov parameters of a two-time-scale distribution. It is shown that the Markov parameters of a two-time-scale distribution can be approximated in terms of the Markov parameters of its fast distribution only. This is an approximation, which deteriorates by a factor of 1/ε for every higher order Markov parameter. In order to use the Markov parameters of the slow distribution in the approximation scheme, an inversion map is introduced by which a two-time-scale distribution and its slow distribution are mapped into new distributions. It is then shown that every Markov parameter of the inverted distribution to within an O(ε) quantity. An approximate expression for the Hankel matrix of the Markov parameters of a two-time-scale distribution is also obtained. This expression is in form of a telescopic series and involves the Markov parameters of the fast distribution only.

Keywords

Hankel matrices; Markov processes; approximation theory; higher order statistics; realisation theory; state-space methods; Hankel matrix; Markov parameter approximation; fast distribution; higher order Markov parameter; inversion map; realization theory; slow distribution; telescopic series; two-time scale distributions; Control system synthesis; Frequency; Reduced order systems; Speech synthesis; Stability; State-space methods; Stochastic processes; System identification;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2003. Proceedings of the 2003

ISSN

0743-1619

Print_ISBN

0-7803-7896-2

Type

conf

DOI

10.1109/ACC.2003.1240546

Filename

1240546