Designing the Hopfield neural network via pole assignment. (English) Zbl 0805.93020

The stability of elquilibria and design of the non-symmetric Hopfield neural network using pole assignment techniques are considered. Stability criterion is derived and bounds of the equilibria are established. It is shown that the design problem is equivalent to an inverse eigenvalue problem. A novel algorithm for the design of Hopfield neural networks with a given equilibrium is presented and illustrated by an example.


93B55 Pole and zero placement problems
Full Text: DOI


[1] BARNETT S., Introduction to Mathematical Control Theory (1985) · Zbl 0576.93001
[2] BURDEN R. L., Numerical Analysis (1989) · Zbl 0671.65001
[3] CODDINGTON E. A., Theory of Ordinary Differential Equations (1955) · Zbl 0064.33002
[4] COHEN M. A., IEEE Trans. Systems, Man Cyber. 13 pp 815– (1983)
[5] GOLUB G. H., Matrix Computation (1989)
[6] DOI: 10.1109/21.87056
[7] HERTZ J., Introuduction to The Theory of Neural Computation
[8] DOI: 10.1016/0893-6080(89)90018-X
[9] DOI: 10.1073/pnas.81.10.3088 · Zbl 1371.92015
[10] IMSL, Fortran Subroutinesfor Mathematical Applications, User’s Manual (1989)
[11] MCCULLOCH W. S., reprinted as Neuralcomputing Foundations of Research 5 pp 115– (1988)
[12] MICHEL A. N., IEEE Trans. Circuits Systems 36 pp 229– · Zbl 0672.94015
[13] MILLER A. N., Ordinary Differential Equations (1982) · Zbl 0552.34001
[14] PONTRYAGIN L. S., Ordinary Differential Equations (1962) · Zbl 0112.05502
[15] YANG , H. , and DILLON , T. S. , 1991 , Some dynamic behaviours of neural networks . Technical Report, Department of Computer Science and Computer Engineering , La Trobe University , Victoria , Australia .
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.