Work

Representation of PDE Systems With Delay and Stability Analysis Using Convex Optimization

Year: 2023

Type: article

Abstract: 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 letter, we show that these results can be combined to obtain a PIE representation of any suitably well-posed 1D PDE model with constant delay. In particular, we represent these delayed PDE systems as coupled systems of 1D and 2D PDEs, obtaining a PIE representation of both subsystems. Taking the feedback interconnection of these PIE subsystems, we then obtain a 2D PIE representation of the 1D PDE with delay. Next, based on the PIE representation, we formulate the problem of stability analysis as convex optimization of positive operators which can be solved using the PIETOOLS software suite. We apply the result to PDE examples with delay in the state and boundary conditions.

Source: IEEE Control Systems Letters

DOI: 10.1109/lcsys.2023.3339095

Authors: Declan S. Jagt, Matthew M. Peet

Institution: Arizona State University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation

Award: War on Boundary Conditions - A Control-Oriented Framework for Partial Differential Equations