Model order reduction for linear time delay systems: A delay-dependent approach based on energy functionals

Abstract

DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

An extended model order reduction technique for linear delay systems

“…In particular, we can freely set S = Q, α o = τ 2ᾱ o , and R = P and α c = τ 2ᾱ c , withᾱ o andᾱ c some positive scalar variables. Substituting these into (3) and (10), while imposing the constraintsQ =ᾱ o Q andP =ᾱ c P , one can recover the matrix inequalities introduced in [13] for τ = 0. The structured/robust reduction is yet to be discussed.…”

“…with Q 11 , Q d,11 andQ 11 respectively the upper left k × k subblocks of Q, Q d andQ, satisfiesÊ o (φ,φ) ≥L o (φ) for allφ ∈ W k . Proof: The proof uses a similar reasoning as the proof of [13,Lemma 4].…”

“…Moreover, for a particular order of the reduced model, a reduced model in terms of delay differential equations has in general the potential to be more accurate than a finite-dimensional approximation of the same order [9]. Therefore, delay-structure preserving methods, i.e., methods that preserve the infinite-dimensional nature of the time delay system during model reduction, *This research has been carried out in the HYDRA project, which has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 675731. have gained much attention [9], [10], [11], [12], [13]. In many cases, however, there is a need to preserve additional properties during model reduction.…”

“…Specifically, the main contribution of this paper is the introduction of a so-called extended balanced truncation procedure for time delay systems. Following [12], [13], bounds on controllability and observability energy functionals are computed and used as a basis for model reduction. However, compared to the results in [13], the current paper introduces additional degrees of freedom in the computation of (bounds on) these functionals through the use of slack variables.…”

“…Following [12], [13], bounds on controllability and observability energy functionals are computed and used as a basis for model reduction. However, compared to the results in [13], the current paper introduces additional degrees of freedom in the computation of (bounds on) these functionals through the use of slack variables. This procedure is motivated by the technique of extended balanced truncation for finite-dimensional systems in [14], [15], which is known to enable structured/robust model reduction [16].…”