Volume 20, Number 3, July-September 2014
|Page(s)||894 - 923|
|Published online||13 June 2014|
On the relation of delay equations to first-order hyperbolic partial differential equations
Department of Mathematics, National Technical University of
Athens, Zografou Campus,
2 Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA
Received: 5 February 2013
Revised: 14 July 2013
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.
Mathematics Subject Classification: 34K20 / 35L04 / 35L60 / 93D20 / 34K05 / 93C23
Key words: Integral delay equations / first-order hyperbolic partial differential equations / nonlinear systems
© EDP Sciences, SMAI, 2014
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