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

Abstract

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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.

How to cite

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Karafyllis, 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 -

References

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