113 citations · 123 across the 15 of their papers we have counts for
16 papers
An Exact Lyapunov Characterization of Regional Rate Performance for Rational Stability
Declan S. Jagt, Matthew M. Peet
Rational stability is a quantitative stability notion for nonlinear ordinary differential equations (ODEs), under which convergence is characterized by a rationally-in-time decayin…
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…
Distributed Sum-of-Squares Programming for Local Stability Analysis of Polynomial PDEs
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…
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…
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.…
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…
-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…
Constructive Representation of Functions in -Dimensional Sobolev Space
Declan S. Jagt, Matthew M. Peet
A new representation is proposed for functions in a Sobolev space with dominating mixed smoothness on an -dimensional hyperrectangle. In particular, it is shown that these funct…
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…
Representation of PDE Systems with Delay and Stability Analysis using Convex Optimization -- Extended Version
Declan S. Jagt, Matthew M. Peet
Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this…
-Gain Analysis of Coupled Linear 2D PDEs using Linear PI Inequalities
Declan S. Jagt, Matthew M. Peet
In this paper, we present a new method for estimating the -gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using s…
Efficient Data Structures for Exploiting Sparsity and Structure in Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS
Declan Jagt, Sachin Shivakumar, Peter Seiler +1
We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables are polynomial i…
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…
PIETOOLS 2022: User Manual
Sachin Shivakumar, Declan Jagt, Danilo Braghini +2
PIETOOLS 2022 manual is a document that describes all the features of the MATLAB toolbox for the analysis and control of Partial Integral Equations (PIEs). The manual is aimed to g…
SOSTOOLS Version 4.00 Sum of Squares Optimization Toolbox for MATLAB
Antonis Papachristodoulou, James Anderson, Giorgio Valmorbida +5
The release of SOSTOOLS v4.00 comes as we approach the 20th anniversary of the original release of SOSTOOLS v1.00 back in April, 2002. SOSTOOLS was originally envisioned as a flexi…