The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
New conditions for global stability of neural networks with application to linear and quadratic programming problems
Abstract
In this paper, we present new conditions ensuring existence, uniqueness, and Global Asymptotic Stability (GAS) of the equilibrium point for a large class of neural networks. The results are applicable to both symmetric and nonsymmetric interconnection matrices and allow for the consideration of all continuous nondecreasing neuron activation functions. Such functions may be unbounded (but not necessarily surjective), may have infinite intervals with zero slope as in a piece-wise-linear model, or both. The conditions on GAS rely on the concept of Lyapunov Diagonally Stable (or Lyapunov Diagonally Semi-Stable) matrices and are proved by employing a class of Lyapunov functions of the generalized Lur'e-Postnikov type. Several classes of interconnection matrices of applicative interest are shown to satisfy our conditions for GAS. In particular, the results are applied to analyze GAS for the class of neural circuits introduced for solving linear and quadratic programming problems. In this application, the principal result here obtained is that these networks are GAS also when the constraint amplifiers are dynamical, as it happens in any practical implementation.>
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Cites
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Cited by
Global convergence of neural networks with discontinuous neuron activations
Forti, M., & Nistri, P. (2003) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/tcsi.2003.818614 · Cited by 451
Self-citationLMI-based approach for asymptotically stability analysis of delayed neural networks
Liao, X., Chen, G., & Sanchez, E. N. (2002) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/tcsi.2002.800842 · Cited by 346
Metadata
- Authors
- Forti, M., & Tesi, A.
- Venue
- IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
- Published
- 1995-07
- Volume
- 42
- Issue
- 7
- Pages
- 354-366
- ISSN
- 1057-7122 (ISSN-L)
- OpenAlex
- W2121752938
- Cited by
- 745
- References
- 17
- FWCI
- 3.62
- Type
- journal article
- Language
- en
- Open access
- closed
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