Slowly varying discrete system x sub /i+1/ = A sub i x sub i

Slowly varying discrete system of matrice

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem

Advanced theoretical and experimental studies in automatic control and information systems

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included

Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. Using Abrikosov's variational procedure, we write the Ginzburg-Landau free energy functional projected on its unstable supspace as an effective model on the triangular lattice of sixfold coordinated sites. For this latter model, we obtain a large class of degenerate equilibrium configurations in one to one correspondence with those previously constructed for the pure XY model on the maximally frustrated dice lattice. The entropy of these states is proportional to the linear size of the system. Finally we show that magnetic interactions between currents provide a degeneracy lifting mechanism.Comment: The final version (as published in Phys. Rev. B). Substantial corrections have been made to Sec.

Exponential stabilization of well-posed systems by colocated feedback

Published versio

Frequency-domain modeling of transients in pipe networks with compound nodes using a Laplace-domain admittance matrix

An alternative to modeling the transient behavior of pipeline systems in the time domain is to model these systems in the frequency domain using Laplace transform techniques. A limitation with traditional frequency-domain pipeline models is that they are only able to deal with systems of a limited class of configuration. Despite the development of a number of recent Laplace-domain network models for arbitrarily configured systems, the current formulations are designed for systems comprised only of pipes and simple node types such as reservoirs and junctions. This paper presents a significant generalization of existing network models by proposing a framework that allows not only complete flexibility with regard to the topological structure of a network, but also, encompasses nodes with dynamic components of a more general class (such as air vessels, valves, and capacitance elements). This generalization is achieved through a novel decomposition of the nodal dynamics for inclusion into a Laplace-domain network admittance matrix. A symbolic example is given demonstrating the development of the network admittance matrix and numerical examples are given comparing the proposed method to the method of characteristics for 11-pipe and 51-pipe networks.Aaron C. Zecchin, Martin F. Lambert, Angus R. Simpson, and Langford B. Whit

Communication Research

Contains reports on seven research projects.Rockefeller FoundationCarnegie Foundatio