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first-order hyperbolic partial differential equations

ESAIM: Control, Optimisation and Calculus of Variations (1)

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On the relation of delay equations to first-order hyperbolic partial differential equations
Iasson Karafyllis, Miroslav Krstic
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 3 / July 2014

Published online by Cambridge University Press:

13 June 2014, pp. 894-923

Print publication:

July 2014
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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.