In this paper the output regulation of a linear distributed parameter system with a nonautonomous periodic exosystem is considered. It is shown that the solvability of the output regulation problem can be characterized by an infinite-dimensional Sylvester differential equation. Conditions are given for the existence of a controller solving the regulation problem along with a method for its cons...

This paper gives an explicit method for computing the resultant of any sparse unmixed bivariate system with given support. We construct square matrices whose determinant is exactly the resultant. The matrices constructed are of hybrid Sylvester and Bézout type. The results extend those in [14] by giving a complete combinatorial description of the matrix. Previous work by D’Andrea [5] gave pure ...

Abstract—A new block algorithm for computing a full rank solution of the Sylvester-observer equation arising in state estimation is proposed. The major Computational Kernels of this algorithm are (i) solutions of ordinary Sylvester equations, in which case each one of the matrices is of much smaller order than that of the system matrix and furthermore, this small matrix can be chosen arbitraril...

This paper develops a mathematical framework for the infinite-dimensional Sylvester equation both in the differential and the algebraic form. It uses the implemented semigroup concept as the main mathematical tool. This concept may be found in the literature on evolution equations occurring in mathematics and physics and is rather unknown in systems and control theories. But it is just systems ...

A fully Sinc-Galerkin method for solving advection-di usion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization which has it's most natural representation in the form of a Sylvester system where the coe cient matrix for the temporal discretization is full. The word \full" often implies a computationally more complex method com...

We discuss certain extremal problems in combinatorial geometry, including Sylvester’s problem and its generalizations.

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building a new DRP scheme in the same time. keywords DRP schemes, Sylvester equation

A constructive procedure to design a single linear functional observer for a time-invariant linear system is given. The proposed procedure is simple and is not based on the solution of a Sylvester equation or on the use of canonical state space forms. Both stable observers or fixed poles observers problems are considered for minimality.