113 citations · 123 across the 15 of their papers we have counts for
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Verifying Well-Posedness of Linear PDEs using Convex Optimization
Declan S. Jagt, Matthew M. Peet
Ensuring that a PDE model is well-posed is a necessary precursor to any form of analysis, control, or numerical simulation. Although the Lumer--Phillips theorem provides necessary…
A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Declan S. Jagt, Matthew M. Peet
Recently, it has been shown that stability analysis and control of coupled Partial Differential Equations (PDEs) in a single spatial variable can be more conveniently performed usi…
Representation and Stability Analysis of 1D PDEs with Periodic Boundary Conditions
Declan Jagt, Sergei Chernyshenko, Matthew Peet
PDEs with periodic boundary conditions are frequently used to model processes in large spatial environments, assuming solutions to extend periodically beyond some bounded interval.…
A PIE Representation of Scalar Quadratic PDEs and Global Stability Analysis Using SDP
Declan Jagt, Peter Seiler, Matthew Peet
It has recently been shown that the evolution of a linear Partial Differential Equation (PDE) can be more conveniently represented in terms of the evolution of a higher spatial der…
A PIE Representation of Coupled Linear 2D PDEs and Stability Analysis using LPIs
Declan S. Jagt, Matthew M. Peet
We introduce a Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in two spatial variables. PIEs are an algebraic state-space representation of…