We detail in this article the development of a delay-robust stabilizing feedback control law for
a linear ordinary differential equation coupled with two linear first order hyperbolic equations …

Partial Integral Equation (PIE) representation of a Partial Differential Equation (PDE) allows
using computationally tractable algorithms for analysis, simulation, and optimal control …

This paper deals with the stability analysis of the reaction–diffusion equation interconnected
with a finite-dimensional system. In this situation, stability is no longer straightforward to …

In this paper, we present a convex formulation of H∞-optimal control problem for coupled
linear ODE-PDE systems with one spatial dimension. First, we reformulate the coupled ODE …

In this paper, we present PIETOOLS, a MATLAB toolbox for the construction and handling of
Partial Integral (PI) operators. The toolbox introduces a new class of MATLAB object, opvar …

Abstract Delay-Differential Equations (DDEs) are the most common representation for
systems with delay. However, the DDE representation is limited. In network models with …

The PIETOOLS 2024 User Manual describes all the features of version 2024 of the MATLAB
toolbox PIETOOLS for the analysis and control of Partial Integral Equations (PIEs). The …

This paper reports necessary stability conditions for a parabolic partial differential equation
(PDE) interconnected through the boundaries to an ordinary differential equation (ODE). We …

This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-
dimensional controller through Dirichlet boundary input and Neumann boundary output …

Recently, a broad class of linear delayed and ODE-PDEs systems was shown to have an
equivalent representation using Partial Integral Equations (PIEs). In this paper, we use this …