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

Matthew Peet (Corresponding author), Sachin Shivakumar, Amritam Das, Siep Weiland

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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
Pages (from-to)132-137
Number of pages6
JournalIFAC-PapersOnLine
Volume52
Issue number2
DOIs
Publication statusPublished - 1 Jun 2019

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Keywords

  • Convex
  • Distributed Parameter Systems
  • LMI
  • PDE

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