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On the relation of delay equations to first-order hyperbolic partial differential equations

Iasson Karafyllis, Miroslav Krstic (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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...

On the stability of neutral-type uncertain systems with multiple time delays

Pin-Lin Liu (2005)

International Journal of Applied Mathematics and Computer Science

The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness...

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