Periodic coprime matrix fraction decompositions

Some Numerical Challenges in Control Theory

We discuss a number of novel issues in the interdisciplinary area of numerical linear algebra and control theory. Although we do not claim to be exhaustive we give a number of problems which we believe will play an important role in the near future. These are : sparse matrices, structured matrices, novel matrix decompositions and numerical shortcuts. Each of those is presented in relation to a ...

Upcoming Numerical Linear Algebra Issues in Systems and Control Theory

We discuss a number of novel issues in the interdisciplinary area of numerical linear algebra and systems and control theory. Although we do not claim to be exhaustive we give a number of \upcoming issues" which we believe will play an important role in the near future. These are : sparse matrices, structured matrices, novel matrix decompositions and numerical shortcuts. Each of those is presen...

New coprime polynomial fraction representation of transfer function matrix

On computing normalized coprime factorizations of periodic systems

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

Smoothness and Periodicity of Some Matrix Decompositions

In this work we consider smooth orthonormal factorizations of smooth matrixvalued functions of constant rank. In particular, we look at Schur, singular value, and related decompositions. Furthermore, we consider the case in which the functions are periodic and study periodicity of the factors. We allow for eigenvalues and singular values to coalesce.