On the relation of delay equations to first-order hyperbolic partial differential equations
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 3, p. 894-923
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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.

DOI : https://doi.org/10.1051/cocv/2014001
Classification:  34K20,  35L04,  35L60,  93D20,  34K05,  93C23
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},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {3},
     year = {2014},
     pages = {894-923},
     doi = {10.1051/cocv/2014001},
     zbl = {1295.35299},
     mrnumber = {3264228},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 20 (2014) no. 3, pp. 894-923. doi : 10.1051/cocv/2014001. http://www.numdam.org/item/COCV_2014__20_3_894_0/

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