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Title: Representation of linear PDEs with spatial integral terms as Partial Integral Equations
In this paper, we present the Partial Integral Equation (PIE) representation of linear Partial Differential Equations (PDEs) in one spatial dimension, where the PDE has spatial integral terms appearing in the dynamics and the boundary conditions. The PIE representation is obtained by performing a change of variable where every PDE state is replaced by its highest, well-defined derivative using the Fundamental Theorem of Calculus to obtain a new equation (a PIE). We show that this conversion from PDE representation to PIE representation can be written in terms of explicit maps from the PDE parameters to PIE parameters. Lastly, we present numerical examples to demonstrate the application of the PIE representation by performing stability analysis of PDEs via convex optimization methods.  more » « less
Award ID(s):
1935453
PAR ID:
10483580
Author(s) / Creator(s):
; ;
Publisher / Repository:
IEEE
Date Published:
Journal Name:
Proceedings of the American Control Conference
ISSN:
0743-1619
ISBN:
979-8-3503-2806-6
Page Range / eLocation ID:
1788 to 1793
Format(s):
Medium: X
Location:
San Diego, CA, USA
Sponsoring Org:
National Science Foundation
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