What is it about?
This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.a. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS, simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions (RQM) is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design
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Why is it important?
This contribution summarizes the original definition of RMS, simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions (RQM) is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.
Perspectives
For the engineering practice, some algebraic operations over the ring have been discussed as well, and control design affairs of the novel proposition are touched by means of a concise illustrative example. Throughout the paper, many examples are presented to illuminate some ideas and results. However, there are many relevant topics that still remain open, for instance to derive other algebraic properties, inclusions, and relationships between some other algebras.
Assoc. Prof. Libor Pekař
Univerzita Tomase Bati ve Zline
Read the Original
This page is a summary of: he Revision and Extension of the RMS Ring for Time Delay Systems, Bulletin of the Polish Academy of Sciences Technical Sciences, January 2017, De Gruyter,
DOI: 10.1515/bpasts-2017-0038.
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