On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations
Abstract
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a single first-order hyperbolic partial differential equation under the effect of measurable inputs acting on the boundary and/or on the differential equation. An illustrative example shows that the conversion of a system described by a single first-order hyperbolic partial differential equation to an integral delay system can simplify considerably the solution of the corresponding robust feedback stabilization problem.
Keywords
Cite
@article{arxiv.1302.1128,
title = {On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations},
author = {Iasson Karafyllis and Miroslav Krstic},
journal= {arXiv preprint arXiv:1302.1128},
year = {2019}
}
Comments
32 pages, submitted for possible publication to ESAIM COCV