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

Iasson Karafyllis; Miroslav Krstic

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 3, page 894-923
- ISSN: 1292-8119

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topKarafyllis, Iasson, and Krstic, Miroslav. "On the relation of delay equations to first-order hyperbolic partial differential equations." ESAIM: Control, Optimisation and Calculus of Variations 20.3 (2014): 894-923. <http://eudml.org/doc/272899>.

@article{Karafyllis2014,

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.},

author = {Karafyllis, Iasson, Krstic, Miroslav},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {integral delay equations; first-order hyperbolic partial differential equations; nonlinear systems; converse Lyapunov results; discontinuous solutions; measurable inputs; robust feedback stabilization problems},

language = {eng},

number = {3},

pages = {894-923},

publisher = {EDP-Sciences},

title = {On the relation of delay equations to first-order hyperbolic partial differential equations},

url = {http://eudml.org/doc/272899},

volume = {20},

year = {2014},

}

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

PB - EDP-Sciences

VL - 20

IS - 3

SP - 894

EP - 923

AB - 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.

LA - eng

KW - integral delay equations; first-order hyperbolic partial differential equations; nonlinear systems; converse Lyapunov results; discontinuous solutions; measurable inputs; robust feedback stabilization problems

UR - http://eudml.org/doc/272899

ER -

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