Ettore F. Infante

Stability in Linear Delay Equations.

Abstract For linear autonomous differential difference equations of retarded or neutral type, necessary and sufficient conditions are given for the zero solution to be stable (hyperbolic) for all values of the delays.

ASYMPTOTIC STABILITY CRITERIA FOR LINEAR SYSTEMS OF DIFFERENCE-DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE AND THEIR DISCRETE ANALOGUES,

Abstract Electrical networks containing lossless transmission lines are often modeled by difference-differential equations of neutral type. This paper finds sufficient conditions for asymptotic stability for linear systems of these equations. Also given is a modification of the direct method of Liapunov for difference equations. This method is applied to finding asymptotic stability criteria for the discrete analogs of the linear system of difference-differential equations.

A Liapunov functional for a matrix neutral difference-differential equation with one delay

Abstract For the matrix neutral difference-differential equation x (t) + A x (t − τ)  Bx(t) + Cx(t − τ) we construct a quadratic Liapunov functional which gives necessary and sufficient conditions for the asymptotic stability of the solutions of that equation. We consider a difference equation approximation of the difference-differential equation, and for this difference equation we construct a Liapunov function from which we obtain the desired Liapunov functional by an appropriate limiting process. The Liapunov functional thus obtained gives the best possible estimate for the rates of growth or decay of the solutions of the matrix neutral difference-differential equation. The results obtained are natural generalizations of previous results obtained for a matrix retarded difference-differential equation with one delay.

Some Results on the Precompactness of Orbits of Dynamical Systems.

Abstract : In order to apply the invariance principle to a dynamical system on a general Banach space, it is necessary to show that positive orbits are precompact. In applications, it is often not too difficult to show that positive orbits are bounded, but this does not imply precompactness unless the underlying space is finite dimensional. Using an approach based on homeomorphic state transformations, the authors obtain certain general criteria for assuring precompactness of positive orbits. These criteria formalize and extend a number of specialized devices previously employed for this purpose. (Author)

On the Stability Properties of an Equation Arising in Reactor Dynamics.

The stability properties are investigated for a system of integro-differential equations which can be applied to one-dimensional, homogeneous reactor dynamics studies.

Money-financed Fiscal Policy in a Growing Economy

The paper examines the trajectories of the economic variables when government expenditures are financed by changes in the money stock. It is shown that government budget balance is not a condition for equilibrium. If the nominal rate of interest changes by about as much as the expected rate of inflation, a rise in real government purchases per capita has the following effects: There will be a positive impact upon output per capita but steady-state output per capita and the capital intensity will decline, and there will be a rise in the inflation tax on real balances and steady-state rate of inflation.