Title :
Further results on the global asymptotic stability of neural networks
Author :
Arik, Sabri ; Tavsanoglu, Vedat
Author_Institution :
Dept. of Electron., Istanbul Univ., Turkey
Abstract :
The classes of I0-stable matrices (denoted by I0 ) and additively diagonally stable matrices (denoted by M0 ) are important in the context of the analysis of absolute stability (ABST) of neural networks. In comments by Kaszkurewicz and Bahaya (see IEEE Trans. Circuits Syst.-I, vol. 42, p. 497-499, August 1995), it was conjectured that the I0 condition of the interconnection matrix T of a neural network is a necessary and sufficient condition for the neural network to be absolutely stable. In a reply by the authors (see IEEE Trans. Circuits Syst.-I, vol. 45, p. 595-596, May 1998) to these comments, it is shown that the M0 condition on T is a sufficient condition for ABST. In this paper the authors clarify the relationship between the classes I0 and M 0. It is proved by an example that the class M0 is a strict subclass of class I0, leading us to draw new conclusions on ABST of neural networks. They also give an example which disproves the conjecture made by Kaszkurewicz and Bhaya
Keywords :
absolute stability; asymptotic stability; matrix algebra; neural nets; absolute stability; additively diagonally stable matrices; global asymptotic stability; interconnection matrix; neural networks; Asymptotic stability; Eigenvalues and eigenfunctions; Equations; Neural networks; Polynomials; Stability analysis;
Conference_Titel :
Circuits and Systems, 2001. ISCAS 2001. The 2001 IEEE International Symposium on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6685-9
DOI :
10.1109/ISCAS.2001.921378