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.

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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