A Generalized LMI Formulation for Input-Output Analysis of Linear Systems of ODEs Coupled with PDEs

Sachin Shivakumar, Amritam Das, Siep Weiland, Matthew Peet

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)

Abstract

In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This work generalizes the sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a recently developed concept of fundamental state and the associated boundary-condition-free representation. The conditions of the generalized KYP are tested using a positive matrix parameterization of bounded operators resulting in a finite-dimensional LMI, the feasibility of which implies prima facie provable passivity or L 2 -gain of the system. No discretization or approximation is involved at any step and there is no conservatism in the theorems. Comparison with other computational methods show that bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.
Original languageEnglish
Title of host publication2019 IEEE 58th Conference on Decision and Control (CDC)
Pages280-285
Number of pages6
ISBN (Electronic)9781728113982
DOIs
Publication statusPublished - 12 Mar 2020
Event58th IEEE Conference on Decision and Control (CDC 2019) - Nice, France
Duration: 11 Dec 201913 Dec 2019
https://cdc2019.ieeecss.org/

Conference

Conference58th IEEE Conference on Decision and Control (CDC 2019)
Abbreviated titleCDC 2019
CountryFrance
CityNice
Period11/12/1913/12/19
Internet address

Keywords

  • dissipative dynamical systems
  • KYP Lemma
  • PDEs
  • Computational complexity

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