TY - JOUR
T1 - Minimal Differential Difference Realizations of Delay Differential, Differential Difference, and Neutral Delay Systems
AU - Peet, Matthew M.
N1 - Funding Information:
Manuscript received September 1, 2020; revised November 1, 2020; accepted November 4, 2020. Date of publication November 17, 2020; date of current version December 15, 2020. This work was supported by the National Science Foundation under Grant CNS-1739990 and Grant CMMI-1931270. Recommended by Senior Editor J. Daafouz.
Publisher Copyright:
© 2017 IEEE.
PY - 2021/10
Y1 - 2021/10
N2 - Delay-Differential Equations (DDEs) are often used to represent control of and over large networks. However, the presence of delay makes the problems of analysis and control of such networks challenging. Recently, Differential Difference Equations (DDFs) have been proposed as a modelling framework which allows us to more efficiently represent the low-dimensional nature of delayed channels in a network or large-scale delayed system. Unfortunately, however, the standard conversion formulae from DDE to DDF do not account for this low-dimensional structure - hence any efficient DDF representation of a large delayed network or system must be hand-crafted. In this letter, we propose an algorithm for constructing DDF realizations of both DDE and DDF systems wherein the dimension of the delayed channels has been minimized. Furthermore, we provide a convenient PIETOOLS implementation of these algorithms and show that the algorithm significantly reduces the complexity of the model for several illustrative examples, including Neutral Delay Systems (NDSs).
AB - Delay-Differential Equations (DDEs) are often used to represent control of and over large networks. However, the presence of delay makes the problems of analysis and control of such networks challenging. Recently, Differential Difference Equations (DDFs) have been proposed as a modelling framework which allows us to more efficiently represent the low-dimensional nature of delayed channels in a network or large-scale delayed system. Unfortunately, however, the standard conversion formulae from DDE to DDF do not account for this low-dimensional structure - hence any efficient DDF representation of a large delayed network or system must be hand-crafted. In this letter, we propose an algorithm for constructing DDF realizations of both DDE and DDF systems wherein the dimension of the delayed channels has been minimized. Furthermore, we provide a convenient PIETOOLS implementation of these algorithms and show that the algorithm significantly reduces the complexity of the model for several illustrative examples, including Neutral Delay Systems (NDSs).
KW - Computational methods
KW - delay systems
KW - distributed parameter systems
KW - modeling
KW - network analysis and control
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U2 - 10.1109/LCSYS.2020.3038758
DO - 10.1109/LCSYS.2020.3038758
M3 - Article
AN - SCOPUS:85096825438
SN - 2475-1456
VL - 5
SP - 1471
EP - 1476
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 4
M1 - 9261405
ER -