Computing input-ouput properties of coupled linear PDE systems

Sachin Shivakumar, Matthew Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose an LMI-based approach to analyze input-output properties of coupled linear PDE systems. This work expands on a newly developed state-space theory for coupled PDEs and extends the positive-real and bounded-real lemmas to infinite dimensional systems. We show that conditions for passivity and bounded L2 gain can be expressed as linear operator inequalities on R× L2. A method to convert these operator inequalities to LMIs by using parameterization of the operator variables is proposed. This method does not rely on discretization and as such, the properties obtained are prima facie provable. We use numerical examples to demonstrate that the bounds obtained are not conservative in any significant sense and that the bounds are computable on desktop computers for systems consisting of up to 20 coupled PDEs.

Original languageEnglish (US)
Title of host publication2019 American Control Conference, ACC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages606-613
Number of pages8
ISBN (Electronic)9781538679265
StatePublished - Jul 1 2019
Event2019 American Control Conference, ACC 2019 - Philadelphia, United States
Duration: Jul 10 2019Jul 12 2019

Publication series

NameProceedings of the American Control Conference
Volume2019-July
ISSN (Print)0743-1619

Conference

Conference2019 American Control Conference, ACC 2019
CountryUnited States
CityPhiladelphia
Period7/10/197/12/19

Fingerprint

Linear systems
Mathematical operators
Parameterization
Personal computers

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Shivakumar, S., & Peet, M. (2019). Computing input-ouput properties of coupled linear PDE systems. In 2019 American Control Conference, ACC 2019 (pp. 606-613). [8814336] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc..

Computing input-ouput properties of coupled linear PDE systems. / Shivakumar, Sachin; Peet, Matthew.

2019 American Control Conference, ACC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 606-613 8814336 (Proceedings of the American Control Conference; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Shivakumar, S & Peet, M 2019, Computing input-ouput properties of coupled linear PDE systems. in 2019 American Control Conference, ACC 2019., 8814336, Proceedings of the American Control Conference, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 606-613, 2019 American Control Conference, ACC 2019, Philadelphia, United States, 7/10/19.
Shivakumar S, Peet M. Computing input-ouput properties of coupled linear PDE systems. In 2019 American Control Conference, ACC 2019. Institute of Electrical and Electronics Engineers Inc. 2019. p. 606-613. 8814336. (Proceedings of the American Control Conference).
Shivakumar, Sachin ; Peet, Matthew. / Computing input-ouput properties of coupled linear PDE systems. 2019 American Control Conference, ACC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 606-613 (Proceedings of the American Control Conference).
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