Title :
Comments on "New conditions for global stability of neural networks with application to linear and quadratic programming problems"
Author :
Liang, Xue-Bin ; Wu, Li-De
Author_Institution :
Dept. of Comput. Sci., Fudan Univ., Shanghai, China
Abstract :
For original paper, see M. Forti and A. Tesi, ibid., vol. 42, pp. 354-66 (1995). This letter makes the following comments: 1) the assumption of all neuron activation functions to vanish at the origin, which is utilized in the proof of the result implying the existence and uniqueness of the network equilibrium point, can be actually omitted; 2) in the infinite sector case, the result of global asymptotic stability (GAS) remains true with respect to the class of increasing (not necessarily strictly) activations, as in the finite sector case. Consequently, a result about absolute stability (ABST) of neural networks, which can represent a generalization of the existing related ones, is also obtained.
Keywords :
absolute stability; asymptotic stability; linear programming; neural nets; nonlinear differential equations; quadratic programming; stability criteria; absolute stability; finite sector case; global asymptotic stability; global stability conditions; infinite sector case; linear programming problems; network equilibrium point; neural networks; neuron activation functions; nonlinear differential equations; quadratic programming problems; Circuits; Design methodology; Digital filters; Finite impulse response filter; Frequency; IIR filters; Low pass filters; Neural networks; Signal processing; Stability;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
