Title :
On the Asymptotical Stability of a 2-D FM-I System
Author :
Zhang Guanglei ; Zhou Tong
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing, China
Abstract :
Two sufficient conditions are derived for the stability of two-dimensional (2D) systems described by the Fornasini-Marchesini first model (FM-I). It is proved that the above sufficient conditions are less conservative than the corresponding conditions of a previous 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.
Keywords :
asymptotic stability; linear matrix inequalities; multidimensional systems; 2D FM-I system; Fornasini-Marchesini first model; LMI based sufficient condition; asymptotical stability; linear matrix inequality; structured singular value; two-dimensional systems; weighted induced-2 matrix norm; Asymptotic stability; Electronic mail; IEEE catalog; Linear matrix inequalities; Numerical simulation; Sufficient conditions; Two dimensional displays; Upper bound; Fornasini-Marchesini first model; stability; structured singular value; two-dimensional system;
Conference_Titel :
Control Conference, 2006. CCC 2006. Chinese
Conference_Location :
Harbin
Print_ISBN :
7-81077-802-1
DOI :
10.1109/CHICC.2006.280774
