Displaying similar documents to “Inertial manifolds for retarded second order in time evolution equations in admissible spaces”

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

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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...

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

A nonsmooth optimisation approach for the stabilisation of time-delay systems

Joris Vanbiervliet, Koen Verheyden, Wim Michiels, Stefan Vandewalle (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic...

On time transformations for differential equations with state-dependent delay

Alexander Rezounenko (2014)

Open Mathematics

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Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

Delay-dependent stability of high-order neutral systems

Yanbin Zhao, Guang-Da Hu (2021)

Kybernetika

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In this note, we are concerned with delay-dependent stability of high-order delay systems of neutral type. A bound of unstable eigenvalues of the systems is derived by the spectral radius of a nonnegative matrix. The nonnegative matrix is related to the coefficient matrices. A stability criterion is presented which is a necessary and sufficient condition for the delay-dependent stability of the systems. Based on the criterion, a numerical algorithm is provided which avoids the computation...