On Algebraic Simplifications of Linear Functional Systems

@article{Cluzeau2009OnAS,
title={On Algebraic Simplifications of Linear Functional Systems},
author={T. Cluzeau and A. Quadrat},
journal={Lecture Notes in Control and Information Sciences},
year={2009},
pages={167-178}
}

In this paper, we show how to conjointly use module theory and constructive homological algebra to obtain general conditions for a matrix R of functional operators (e.g., differential/shift/time-delay operators) to be equivalent to a block-triangular or blockdiagonal matrix \(\bar{R}\) (i.e., conditions for the existence of unimodular matrices V and W satisfying that \(\bar{R} = V RW\)). These results allow us to simplify the study of many linear functional systems – particularly differential… Expand