Quantitative theorems for regular systems of equations

Quantitative theorems for regular systems of equations

The regulator equations for regular linear systems

We investigate the state feedback regulator problem for exponentially stable plants belonging to the class of regular linear systems. The plant is driven by a linear completely unstable exosystem via a disturbance signal. The exosystem also generates the reference signal for the plant output. The state feedback regulator problem is to design a controller that has access to the states of the exo...

Oscillation theorems for systems of linear differential equations

On Equations for Regular

We consider systems of equations of the form Xi=,IJ,a l &~LJ& i=l,...,n where A is the underlying alphabet, the Xi are variables, the Pi.0 are boolean functions in the variables J&B and each & is either the empty word or the empty set. The symbols and u denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equat...

Tauberian Theorems for Matrix Regular Variation.

Karamata's Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated.