On the relation of delay equations to first-order hyperbolic partial differential equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 894-923.

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.

DOI : 10.1051/cocv/2014001
Classification : 34K20, 35L04, 35L60, 93D20, 34K05, 93C23
Mots-clés : integral delay equations, first-order hyperbolic partial differential equations, nonlinear systems 
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Karafyllis, Iasson; Krstic, Miroslav. On the relation of delay equations to first-order hyperbolic partial differential equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 894-923. doi : 10.1051/cocv/2014001. http://archive.numdam.org/articles/10.1051/cocv/2014001/

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