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On the relation of delay equations to first-order hyperbolic partial differential equations

Published online by Cambridge University Press:  13 June 2014

Iasson Karafyllis  and
Miroslav Krstic
Iasson Karafyllis
Affiliation:
Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece. iasonkar@central.ntua.gr
Miroslav Krstic
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA; krstic@ucsd.edu
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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. Illustrative examples show 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 stability analysis and the solution of robust feedback stabilization problems.

Keywords

Integral delay equationsfirst-order hyperbolic partial differential equationsnonlinear systems
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 20 , Issue 3 , July 2014 , pp. 894 - 923
Copyright
© EDP Sciences, SMAI, 2014

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