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},
year = {2014},
publisher = {EDP-Sciences},
volume = {20},
number = {3},
doi = {10.1051/cocv/2014001},
mrnumber = {3264228},
zbl = {1295.35299},
language = {en},
url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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, Tome 20 (2014) no. 3, pp. 894-923. doi: 10.1051/cocv/2014001
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