Second-order bounds on the domain of attraction and the rate ofconvergence of nonlinear dynamical systems and neural networks

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.     

A delta transform approach to loop gain-phase shaping design of robust digital control systems

This paper addresses the existence of loop gain-phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum-phase, continuous-time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete-time systems using the Δ-transform, a transform method that applies to both continuous-time and discrete-time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital control problems.     

Base-type languages: Program design by upper semantic approximation

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 140–155, July–August 1994.     

Fault trees—Problems and the modern state of investigations

Published in Kibernetika i Sistemnyi Analiz, No. 3, pp. 128–150, May–June, 1994.     

Statistical synchronization among participants in real-time multimedia conferencing

In this paper, an algorithm to determine the set of packets generated continuously and periodically from different participants that are arriving at a node either for mixing at the master of a conference, or for simply playing back at a regular participant of a conference, is proposed. The essence of the algorithm is to estimate the expected packet arrival time (or reference time) for each participant. With the reference time at hand, the maximum jitter and the optimum waiting time for a mixer to wait packets from all participants can be determined. An enhancement to improve synchronization which deals with the estimation of the time offsets between the individual periods of the sources and the period of the receiver is also presented. The error of the proposed algorithm is enumerated by the Chernoff bound and demonstrated by simulation and is shown to be acceptable in practical application. The algorithm can also be employed when traffic sources operate with different periods.     

Local variations of the dynamic elastic modulus around running cracks

The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena.