6 papers
A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Declan S. Jagt, Matthew M. Peet
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of…
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…
A Distributed SOS Program For Local Stability Analysis of Polynomial PDEs in the PIE Representation
Carl R Richardson, Declan S Jagt, Matthew M Peet +1
It has recently been shown that the evolution of a state, described by a Partial Differential Equation (PDE), can be more conveniently represented as the evolution of the state's h…
PIETOOLS 2025: User Manual
Sachin Shivakumar, Declan Jagt, Danilo Braghini +3
The PIETOOLS 2025 User Manual describes all the features of version 2025 of the MATLAB toolbox PIETOOLS for the analysis and control of Partial Integral Equations (PIEs). The manua…
Lyapunov Functions can Exactly Quantify Rate Performance of Nonlinear Differential Equations
Declan S. Jagt, Matthew M. Peet
Pointwise-in-time stability notions for Ordinary Differential Equations (ODEs) provide quantitative metrics for system performance by establishing bounds on the rate of decay of th…
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.…