A ring for description and control of time-delay systems

Abstract

This contribution aims a revision and extension of the ring of retarded quasipolynomial meromorphic functions (RMS) for description and control of time-delay systems (TDS). The original definition has some significant drawbacks - especially, it does not constitute a ring. Our new definition extends the usability to neutral TDS and to those with distributed delays. As first, basic algebraic notions useful for this paper are introduced. A concise overview of algebraic methods for TDS follows. The original and the revised definitions of the ring together with some its properties finish the contribution. There are many illustrative examples that explain introduced terms and findings throughout the paper.