Showing papers by "Anthony N. Michel published in 1987"

Stability Results for Neural Networks

Abstract: In the present paper we survey and utilize results from the qualitative theory of large scale interconnected dynamical systems in order to develop a qualitative theory for the Hopfield model of neural networks. In our approach we view such networks as an interconnection of many single neurons. Our results are phrased in terms of the qualitative properties of the individual neurons and in terms of the properties of the interconnecting structure of the neural networks. Aspects of neural networks which we address include asymptotic stability, exponential stability, and instability of an equilibrium; estimates of trajectory bounds; estimates of the domain of attraction of an asymptotically stable equilibrium; and stability of neural networks under structural perturbations.

Stability analysis of interconnected dynamical systems: Hybrid systems involving operators and difference equations

Abstract: We address the stability analysis of interconnected feedback systems of the type depicted in Fig. 1, which consists of a linear interconnection of l subsystems. Each subsystem is a feedback system in its own right, consisting of a local plant (which is described by an operator L_i ) and of a digital controller (which is described by a system of difference equations and which includes A/D and D/A converters). We establish conditions for the attractivity, asymptotic stability, asymptotic stability in the large, and boundedness of solutions for such systems. The hypotheses of our results are phrased in terms of the I/O properties of the operators L_i and of the entire interconnected system, and in terms of the Lyapunov stability properties of digital controllers described by the indicated difference equations. In all cases, our results allow a stability analysis of complex interconnected systems in terms of the qualitative properties of the simpler free subsystems and in terms of the properties of the system interconnecting structure. The applicability of our results is demonstrated by means of a specific example (Fig. 2).

On dynamic effects of quanization and overflow nonlinearities in digital feedback control systems

Abstract: The stability of SISO digital feedback systems is considered. These systems contain a linear dynamic plant, a digital controller and suitable D/A and A/D connections. The design of such a system is normally accomplished by ignoring the nonlinear effects caused by quantization and overflow truncation. It is shown (by simulations of specific examples) that quantization can lead to loss of asymptotic stability. Instead, our results prove that one has convergence to a small neighborhood of the origin. For large initial conditions it is shown that overflow effects can lead to unbounded solutions.