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math.OC2026
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…
math.OC2026
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…
math.OC2024
-Optimal Estimator Synthesis for Coupled Linear 2D PDEs using Convex Optimization
Declan S. Jagt, Matthew M. Peet
Any suitably well-posed PDE in two spatial dimensions can be represented as a Partial Integral Equation (PIE) -- with system dynamics parameterized using Partial Integral (PI) oper…