Narrow Results

We derive algorithms that compute a balanced state representation from the differential equation describing a finite-dimensional linear system.

In this paper we consider the abstract minimization problem:

This paper presents a simulation method of self-similar traffic and a type of TCP traffic simulators based on autocorrelation sequences. The impulse function of a simulator is carried out. The parameter estimations for modeling the impulse function of the simulator are determined by multidimensional nonlinear least squares fitting. The existence and the uniqueness of solutions for the multidimensional nonlinear least squares are proved based on convex analysis.

The aim of this paper is to use the theory of biorthogonal polynomials to derive many algorithms for solving a system of linear equations in a unified framework. These algorithms include extrapolation and projection algorithms, the most important ones being conjugate gradient-type algorithms. New algorithms are also obtained.

In this paper, an algorithmic technique for investigating the necessary and sufficient conditions for two homogeneous matrix pencils sF₁ - ŝG₁ and sF₂ - ŝG₂ to be bilinear equivalent is provided. The proposed problem is very interesting since the applications are merely numerous.

This paper deals with the problem of Disturbance Rejection by Dynamic Output Feedback. It aims at proposing new geometric and structural characterizations for the Fixed Poles of this problem, i.e. the greatest set of fixed poles that are present in the closed loop system for all possible solution (whatever be the way used to find this solution). We also propose minimal solutions to the problem in terms of the fixed poles, i.e., solutions for which all the poles are freely placed, except the fixed poles of the problem. As a corollary, we propose a structural necessary and sufficient condition for the existence of internally stable solutions, which generalizes the sufficient structural condition proposed by Basile and Marro. It has to be noted that no restrictive assumption is made on the system concerning controllability or observability. Our results are established under the natural and unrestrictive assumption that the overall state description is minimal, i.e. controllable and observable, but with respect to all the inputs (control and disturbance) and all the outputs (controlled output and measurement).

This paper presents an algorithm for the row reduction of nonsingular polynomial matrices. The algorithm is based on polynomial matrix to state space and vice versa conversions, avoids computation of elementary polynomial operations, and relies on well-proven methods of numerical linear algebra such as Householder transformations and Hessenberg forms