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...

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

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.

We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of a unique solution is obtained. We improved the results obtained by Isakov and Sylvester (1994) for the same problem.

This paper presents the solution of the constrained Sylvester equation associated to linear descriptor systems. This problem has been recently studied in [1], where sufficient conditions for the existence of the solution are given. In the present paper, a simple and direct method is developed to solve this problem. This method shows that the conditions given in [1] are necessary and sufficient.

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.