The upper bound of the second-order modes of linear state-space systems [digital filter example]

Author

Koshita, Shunsuke ; Abe, Masahide ; Kawamata, Masayuki

Author_Institution

Dept. of Electron. Eng., Tohoku Univ., Sendai, Japan

fYear

2005

fDate

23-26 May 2005

Firstpage

968

Abstract

This paper describes the upper bound of the second-order modes of linear state-space systems. With the help of the bounded-real Riccati equations and bilinear transformation, it is proved that the second-order modes of continuous-time or discrete-time systems are all bounded by the system gain. As an application of this theory, a new formula for evaluating the minimum attainable value of coefficient sensitivity of digital filters is presented. This new formula shows the excellent performance of digital filters with a minimum coefficient sensitivity structure.

Keywords

Riccati equations; continuous time systems; digital filters; discrete time systems; modal analysis; quantisation (signal); sensitivity analysis; state-space methods; Gramians; bilinear transformation; bounded-real Riccati equations; coefficient sensitivity minimum attainable value; continuous-time systems; digital filter coefficient sensitivity; discrete-time systems; linear state-space systems; minimum quantization effects; second-order modes upper bound; system gain bounded second-order modes; Control theory; Controllability; Digital filters; Digital signal processing; Eigenvalues and eigenfunctions; Noise reduction; Observability; Riccati equations; Transfer functions; Upper bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2005. ISCAS 2005. IEEE International Symposium on

Print_ISBN

0-7803-8834-8

Type

conf

DOI

10.1109/ISCAS.2005.1464751

Filename

1464751