On the asymptotical stability of a 2-D FM-I system

被引：0

作者：

Zhang Guanglei ^{[1
]}

Zhou Tong ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Automat, Beijing 100084, Peoples R China

来源：

2006 CHINESE CONTROL CONFERENCE, VOLS 1-5 | 2006年

关键词：

Fornasini-Marchesini first model; stability; structured singular value; two-dimensional system;

D O I：

暂无

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Two sufficient conditions are derived for the stability of two-dimensional (2-D) systems described by the Fomasini-Marchesini first model (FM-I). It is proved that the above sufficient conditions are less conservative than the corresponding conditions of a recent paper. It is also observed that all of the available sufficient conditions can be regarded as upper bounds of the structured singular value (SSV) of a related matrix. Moreover, it is proved that when a weighted induced-2 matrix norm is adopted, the satisfaction of a norm based sufficient condition implies that of a linear matrix inequality (LMI) based one. Numerical simulations have also been performed to compare the conservatism of all the available sufficient conditions. It is found that there is an LMI based sufficient condition which outperforms all the other sufficient conditions.

引用

页码：2099 / +

页数：2

共 9 条

[1] 2S COMPLEMENT QUANTIZATION IN 2-DIMENSIONAL STATE-SPACE DIGITAL-FILTERS
BOSE, T
TRAUTMAN, DA
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1992, 40 (10) : 2589 - 2592
[2] STABILITY OF THE 2-D STATE-SPACE SYSTEM WITH OVERFLOW AND QUANTIZATION
BOSE, T
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-ANALOG AND DIGITAL SIGNAL PROCESSING, 1995, 42 (06): : 432 - 434
[3] STATE-SPACE REALIZATION THEORY OF 2-DIMENSIONAL FILTERS
FORNASINI, E
MARCHESINI, G
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1976, 21 (04) : 484 - 492
[4] MULTIDIMENSIONAL LINEAR ITERATIVE CIRCUITS - GENERAL PROPERTIES
GIVONE, DD
ROESSER, RP
[J]. IEEE TRANSACTIONS ON COMPUTERS, 1972, C 21 (10) : 1067 - &
[5] Simple criteria for stability of two-dimensional linear systems
Hu, GD
Liu, MZ
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2005, 53 (12) : 4720 - 4723
[6] Stability of 2-D systems described by the fornasini-Marchesini first model
Kar, H
Singh, V
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2003, 51 (06) : 1675 - 1676
[7] THE COMPLEX STRUCTURED SINGULAR VALUE
PACKARD, A
DOYLE, J
[J]. AUTOMATICA, 1993, 29 (01) : 71 - 109
[8] On the Bose-Trautman condition for stability of two-dimensional linear systems
Su, YF
Bhaya, A
[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (07) : 2069 - 2070
[9] ZHOU T, IN PRESS IEEE T SIGN

← 1 →