Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs

Matthew Peet, Sachin Shivakumar, Amritam Das, Seip Weiland

Research output: Contribution to journalConference article

Abstract

We present a computational framework for stability analysis of systems of coupled linear Partial-Differential Equations (PDEs). The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichlet, Neuman and mixed boundary conditions. The results in this paper apply to systems with a single spatial variable. We exploit a new concept of state for PDE systems which allows us to include the boundary conditions directly in the dynamics of the PDE. The resulting algorithms are implemented in Matlab, tested on several motivating and illustrative examples, and the codes have been posted online. Numerical testing indicates the approach has little or no conservatism for a large class of systems and can analyze systems of up to 20 coupled PDEs.

Original languageEnglish (US)
Pages (from-to)132-137
Number of pages6
JournalIFAC-PapersOnLine
Volume52
DOIs
StatePublished - Jun 1 2019
Event3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations, CPDE 2019 - Oaxaca, Mexico
Duration: May 20 2019May 24 2019

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Partial differential equations
Boundary conditions
Testing

Keywords

  • Convex
  • Distributed Parameter Systems
  • LMI
  • PDE

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Discussion paper : A new mathematical framework for representation and analysis of coupled PDEs. / Peet, Matthew; Shivakumar, Sachin; Das, Amritam; Weiland, Seip.

In: IFAC-PapersOnLine, Vol. 52, 01.06.2019, p. 132-137.

Research output: Contribution to journalConference article

Peet, Matthew ; Shivakumar, Sachin ; Das, Amritam ; Weiland, Seip. / Discussion paper : A new mathematical framework for representation and analysis of coupled PDEs. In: IFAC-PapersOnLine. 2019 ; Vol. 52. pp. 132-137.
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