A Behavioral Approach to the Control of Discrete Linear Repetitive Processes

This paper formulates the theory of linear discrete time repetitive processes in the setting of behavioral systems theory. A behavioral, latent variable model for repetitive processes is developed and for the physically defined inputs and outputs as manifest variables, a kernel representation of their behavior is determined. Conditions for external stability and controllability of the behavior are then obtained. A sufficient condition for stabilizability is also developed for the behavior and it is shown under a mild restriction that, whenever the repetitive system is stabilizable, a regular constant output feedback stabilizing controller exists. Next a notion of eigenvalues is defined for the repetitive process under an action of a closed loop controller. It is then shown how under controllability of the original repetitive process, an arbitrary assignment of eigenvalues for the closed loop response can be achieved by a constant gain output feedback controller under the above restriction. These results on the existence of constant gain output feedback controllers are among the most striking properties enjoyed by repetitive systems, discovered in this paper. Results of this paper utilize the behavioral model of the repetitive process which is an analogue of the 1D equivalent model of the dynamics studied in earlier work on repetitive processes

Three-dimensional stability of the solar tachocline

The three-dimensional, hydrodynamic stability of the solar tachocline is investigated based on a rotation profile as a function of both latitude and radius. By varying the amplitude of the latitudinal differential rotation, we find linear stability limits at various Reynolds numbers by numerical computations. We repeated the computations with different latitudinal and radial dependences of the angular velocity. The stability limits are all higher than those previously found from two-dimensional approximations and higher than the shear expected in the Sun. It is concluded that any part of the tachocline which is radiative is hydrodynamically stable against small perturbations.Comment: 6 pages, 8 figures, accepted by Astron. & Astrophy

Causal and Stable Input/Output Structures on Multidimensional Behaviours

In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable called "time". We define in a natural way causality and stability on input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the Pc operator defining the behaviour (Bc)0,y We also quote results which in effect characterise time autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix. We prove this result for the 2D case and for the case of a single equation; for the general case it requires solution of an open problem concerning the geometry of a particular set in Cn. In order to characterize input/output stability we also develop new results on inclusions of kernels, freeness of variables, and closure with respect to S,S' and associated spaces, which are of independent interest. We also discuss stability of autonomous behaviours, which we beleive to be governed by a corresponding condition

On control laws for discrete linear repetitive processes with dynamic boundary conditions

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations in the sequence of pass profiles produced which increase in amplitude in the pass-to-pass direction and cannot be controlled by application of standard control laws. Here we give new results on the design of physically based control laws for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Spurious correlation in estimation of the health production function: A note

In this paper, we address the issue of spurious correlation in the production of health in a systematic way. Spurious correlation entails the risk of linking health status to medical (and nonmedical) inputs when no links exist. This note first presents the bounds testing procedure as a method to detect and avoid spurious correlation. It then applies it to a recent contribution by Lichtenberg (2004), which relates longevity in the United States to pharmaceutical innovation and public health care expenditure. The results of the bounds testing procedure show longevity to be linearly related to these two factors. Therefore, the estimates reported by Lichtenberg (2004) cannot be said to be result of spurious correlation, to the contrary, they very likely reflect an effective relationship, at least for the United States.Health; Life expectancy, Innovation, Pharmaceuticals, Health care expenditure, Cointegration

Spurious correlation in estimation of the health production function: A note

In this paper, we address the issue of spurious correlation in the production of health in a systematic way. Spurious correlation entails the risk of linking health status to medical (and nonmedical) inputs when no links exist. This note first presents the bounds testing procedure as a method to detect and avoid spurious correlation. It then applies it to a recent contribution by Lichtenberg (2004), which relates longevity in the United States to pharmaceutical innovation and public health care expenditure. The results of the bounds testing procedure show longevity to be related to these two factors. Therefore, the estimates reported by Lichtenberg (2004) cannot be said to be result of spurious correlation, to the contrary, they very likely reflect an effective relationship, at least for the United States.Health; Life expectancy; Innovation; Pharmaceuticals; Health care expenditure; Cointegration

Out-of-Pocket Prescription Drug Expenditures and Public Prescription Drug Programs

Canadian household prescription drug expenditures are studied using different years of the Statistics Canada Family Expenditure Survey. Master files are used, expanding the number of available years and permitting provincial rather than regional identifiers. Nonparametric Engel curves are estimated. Difference-in-difference mean and 80th percentile regressions examine budget shares by low-income and high-income households before and after the introduction of provincial prescription drug programs. The evidence is consistent with the view that unlike senior prescription drug subsidies, nonsenior prescription drug subsidies are probably more redistributive than an equal-cost proportional income transfer.Prescription drug benefits; incidence

Characteristics of Separated Flow Regions Within Altitude Compensating Nozzles Final Report

Characteristics of separated flow regions within altitude compensating nozzle

Out-of-Pocket Prescription Drug Expenditures and Public Prescription Drug Programs

Canadian household prescription drug expenditures are studied using different years of the Statistics Canada Family Expenditure Survey. Master files are used, expanding the number of available years and permitting provincial rather than regional identifiers. Nonparametric Engel curves are estimated. Difference-in-difference mean and 80th percentile regressions examine budget shares by low-income and high-income households before and after the introduction of provincial prescription drug programs. The evidence is consistent with the view that unlike senior prescription drug subsidies, nonsenior prescription drug subsidies are probably more redistributive than an equal-cost proportional income transfer.Prescription drug benefits; incidence