Dynamical systems with saturation nonlinearities: analysis and design
type: Item
instance of: scholarly article
title: Dynamical systems with saturation nonlinearities: analysis and design
zbMATH Open document ID: 0806.93051
author: Derong Liu
author: Anthony N. Michel
published in: Lecture Notes in Control and Information Sciences
publication date: 1994-08-30T00:00:00Z
review text: The book is more on the circuit theory, esp. the neural network theory than on the control or systems theory. The senior author was the editor of IEEE Transactions on Circuits and Systems. Some basic results are as follows. For a class of linear continuous-time dynamical system with saturation the null solution will be globally asymptotically stable if some measure of the state matrix is negative. For discrete-time systems are constructed two Lyapunov functions. For a discrete-time system with saturation are given the conditions under which it can be stabilized by constrained controllers. The least restrictive criterion for testing limit cycles in fixed-point digital filters is given. Several sufficient conditions for the global asymptotic stability of zero state equilibrium of 2-D digital filters subject to overflow nonlinearities are established. For quadratic forms are presented necessary and sufficient criteria for the construction of Lyapunov functions. The next are considered neural networks which have the structure of analog Hopfield neural networks. All equilibria are then located and their stability determined. The synthesis procedure for associative memories which guarantee to store the desired patterns. Synthesis procedure for artificial neural networks with prespecified interconnection structure is presented.
reviewed by: A.Vaněček
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 68T10
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 626634
zbMATH Keywords: neural network theory
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: Hopfield neural networks
MaRDI profile type: Publication
DOI: 10.1007/BFB0032146
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description: scientific article; zbMATH DE number 626634