11 papers
Dual Representations and Proxy Characterization of Norm for Partial Integral Equations
Danilo Braghini, Tristan Thomas, Sachin Shivakumar +2
Duality and dual representations are essential tools for systems theory and controller synthesis. For any finite-dimensional causal linear time-invariant (CLTI) system, there exist…
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…
Static Output Feedback Stabilization of Linear Systems with Multiple Delays
Danilo Braghini, Eduardo S. Tognetti, Matthew M. Peet
This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordina…
Picard Iteration for Parameter Estimation in Nonlinear Dynamic Models of Aircraft and Spacecraft
Aleksandr Talitckii, Matthew Peet
The attitude dynamics of aircraft and spacecraft exhibit significantly nonlinear behaviour. In spacecraft, torque is generated through reaction wheels and control moment gyros. In…
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…
Hierarchical Stability and Lyapunov Conditions for Linear PDEs
Matthew M. Peet
Unlike ordinary differential equations (ODEs), linear partial differential equations (PDEs) admit multiple non-equivalent notions of stability. This variety makes interpretation of…
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 Estimation of Linear Delayed and PDE Systems
Danio Braghini, Sachin Shivakumar, Matthew M. Peet
The norm is a commonly used performance metric in the design of estimators. However, -optimal estimation of most PDEs is complicated by the lack of transfer function and…