English

On the Relation of Delay Equations to First-Order Hyperbolic Partial Differential Equations

Optimization and Control 2019-02-20 v1 Systems and Control Analysis of PDEs Dynamical Systems

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

R2 v1 2026-06-21T23:21:16.565Z