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 equations, first-order hyperbolic partial differential equations, nonlinear systems

@article{COCV_2014__20_3_894_0, author = {Karafyllis, Iasson and Krstic, Miroslav}, title = {On the relation of delay equations to first-order hyperbolic partial differential equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {894--923}, publisher = {EDP-Sciences}, volume = {20}, number = {3}, year = {2014}, doi = {10.1051/cocv/2014001}, mrnumber = {3264228}, zbl = {1295.35299}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014001/} }

TY - JOUR AU - Karafyllis, Iasson AU - Krstic, Miroslav TI - On the relation of delay equations to first-order hyperbolic partial differential equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2014 SP - 894 EP - 923 VL - 20 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014001/ DO - 10.1051/cocv/2014001 LA - en ID - COCV_2014__20_3_894_0 ER -

%0 Journal Article %A Karafyllis, Iasson %A Krstic, Miroslav %T On the relation of delay equations to first-order hyperbolic partial differential equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2014 %P 894-923 %V 20 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014001/ %R 10.1051/cocv/2014001 %G en %F COCV_2014__20_3_894_0

Karafyllis, Iasson; Krstic, Miroslav. On the relation of delay equations to first-order hyperbolic partial differential equations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 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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