Showing papers by "Anthony N. Michel published in 1993"

Cellular neural networks for associative memories

Abstract: A synthesis procedure for designing nonsymmetric cellular neural networks (CNN) with a predetermined local interconnection structure that will store a set of desired bipolar vectors as memory points is presented. A specific case of constructing Chinese characters is presented to demonstrate the applicability of the results. Simulation results show that all the vectors corresponding to 50 commonly used Chinese characters are reachable memory vectors of the synthesized CNN. >

Robustness and Perturbation Analysis of a Class of Nonlinear Systems with Applications to Neural Networks

Abstract: We study robustness properties of a large class of nonlinear systems, by addressing the following question: given a nonlinear system with specified asymptotically stable equilibria, under what conditions will a perturbed model of the system possess asymptotically stable equilibria which are close (in distance) to the asymptotically stable equilibria of the unperturbed system? In arriving at our results, we establish robustness stability results for the perturbed systems considered and we determine conditions which ensure the existence of asymptotically stable equilibria of the perturbed system which are near the asymptotically stable equilibria of the original unperturbed system. These results involve quantitative estimates of the distance between the corresponding equilibrium points of the unperturbed and perturbed systems. We apply the above results in the qualitative analysis of a large class of artificial neural networks.

Necessary and sufficient conditions for the stability of interval matrices

Abstract: Establishes a set of new sufficient conditions for the Hurwitz and Schur stability of interval matrices The authors use these results to establish necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices The authors relate the above results to the existence of quadratic Lyapunov functions for linear time-invariant systems with interval-valued coefficient matrices Using the above results, the authors develop an algorithm to determine the Hurwitz and the Schur stability properties of interval matrices It is shown that the authors' algorithm is applicable to very large classes of interval matrices and the authors prove that for such classes, the algorithm terminates in a finite number of steps The authors demonstrate the applicability of their results by means of two specific examples >

Analysis and synthesis of a class of neural networks with sparse interconnections

Abstract: The authors present results for the analysis and synthesis of a class of neural networks with sparse or partial interconnecting structure. The, design procedure guarantees to synthesize neural networks with arbitrarily predetermined sparse interconnection structures and to store any given set of desired bipolar patterns as memories. It is shown that a sufficient condition for the existence of a design for neural networks with sparse interconnection is self-feedback for every neuron in the network. Several specific examples are included to demonstrate the applicability of the methodology. >

Bursting Phenomena in Extended-Least Squares Based Self-Tuning Control

Abstract: In this paper, bursting phenomena inherent to extended least-squares based self-tuning control are analyzed. It is shown that in the absence of external excitation and without imposing structural conditions on the system model, bursts of the tracking error and consequently drift of the parameter estimates are possible. Our analysis reveals the basic principle of learning and adaptation mechanisms: every increase of system disorder causes corresponding increases of system intelligence. On the other hand, every increase of system precision causes decreases of system intelligence.

Controllability and observability of a class of linear, time-invariant systems with interval plants

Abstract: We establish necessary and sufficient conditions for the controllability of single input/multi output linear time-invariant systems with interval plants, and for the observability of multi input/single output linear time-invariant systems with interval plants. In arriving at our results, we determine allowable plant uncertainty bounds for controllability and observability. To demonstrate the applicability of our results, two specific examples are considered. >

Robustness analysis of a class of neural networks

Abstract: We present a robustness analysis result for a class of neural networks. Specifically, we assume a set of bipolar vectors to be memories for a network, and we establish a sufficient condition under which the given set of vectors are also memories of the original network after perturbations on its parameters. >

Analysis and synthesis of sparsely connected feedback neural networks

Abstract: Presents results for the analysis and synthesis of a class of neural networks with sparse connections. The authors' design procedure guarantees to synthesize neural networks with arbitrarily predetermined sparse connection structures and to store a given set of desired bipolar patterns. >

Sufficient Conditions for Hurwitz and Schur Stability of Interval Matrices

Abstract: We investigate the Hurwitz and Schur stability of interval matrices using Lyapunov's Second Method and interval analysis techniques. Previous results require a check of the definiteness of 2n(n?1)/2 corners of a certain interval matrix. The present results require a check of the definiteness of only 2n?1 corners.

Sparsely Interconnected Artificial Neural Networks for Associative Memories

Abstract: We develop in the present paper a design procedure for neural networks with sparse coefficient matrices. Our results guarantee that the synthesized neural networks have predetermined sparse interconnection structures and store any set of desired memory patterns as reachable memory vectors. We show that a sufficient condition for the existence of a sparse neural network design is self feedback for every neuron in the network. Our design procedure for neural networks with sparse interconnecting structure can take into account various problems encountered in VLSI realizations of such networks. For example, our procedure can be used to design neural networks with few or without any line-crossings resulting from the network interconnections. Several specific examples are included to demonstrate the applicability of the methodology advanced herein.

Robustness analysis and design of sparsely interconnected neural networks

Abstract: We first conduct an analysis of the robustness properties of a class of neural networks with applications to associative memories Specifically, for a network with nominal parameters storing a set of desired bipolar memories, we establish sufficient conditions under which the same set of bipolar memories is also stored in the network with perturbed parameters This result enables us to establish a design procedure for neural networks whose stored memories are invariant under perturbations Our design procedure is capable of generating artificial neural networks with prespecified sparsity constraints and in particular, is applicable in the design of cellular neural networks for associative memories >

Asymptotic stability of two-dimensional digital filters with overflow nonlinearities

Abstract: Lyapunov's second method is used to establish several sufficient conditions for the global asymptotic stability of the trivial solution of 2D quarter plane state-space digital filters which are endowed with a general class of overflow nonlinearities. The authors' results are generalized to a class of m-D (multi-dimensional) digital filters endowed with overflow nonlinearities. Two specific examples are considered to demonstrate the applicability of their results. >

Stability of dynamical systems determined by differential inequalities with applications to nonlinear circuits

Abstract: We develop a Lyapunov stability theory for finite dimensional continuous-time dynamical systems described by a system of first order ordinary differential inequalities. We utilize this theory to establish sufficient robust stability criteria for a large class of finite dimensional, continuous-time dynamical systems described by systems of ordinary differential equations. We demonstrate the applicability of the methodology advanced herein by means of a specific example which has been considered in the literature. In terms of computational complexity and conservatism of stability criteria, the present results frequently offer improvements over existing results. >