Summary
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 time-delay systems – appearing in control theory and mathematical physics.
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Cluzeau, T., Quadrat, A. (2009). On Algebraic Simplifications of Linear Functional Systems. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_15
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DOI: https://doi.org/10.1007/978-3-642-02897-7_15
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