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The problem of the decentralized robust tracking and model following is considered for a class of uncertain large scale systems including time-varying delays in the interconnections. On the basis of the Razumikhin-type theorem and the Lyapunov stability theory, a class of decentralized memoryless local state feedback controllers is proposed for robust tracking of dynamical signals. It is shown that by employing the proposed decentralized robust tracking controllers, one can guarantee that the tracking...

Dégénérescence des systèmes discrets et application à un problème de commande

P. Charrier (1976)

Banach Center Publications

Delay differential systems with discontinuous initial data and existence and uniqueness theorems for systems with impulse and delay.

Krishna, S.V., Anokhin, A.V. (1994)

Journal of Applied Mathematics and Stochastic Analysis

Delay differential systems with time-varying delay: new directions for stability theory

James Louisell (2001)

Kybernetika

In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the delay function,...

Delay makes problems in population modelling

Smítalová, Kristína (1986)

Equadiff 6

Delay Model of Hematopoietic Stem Cell Dynamics: Asymptotic Stability and Stability Switch

F. Crauste (2009)

Mathematical Modelling of Natural Phenomena

A nonlinear system of two delay differential equations is proposed to model hematopoietic stem cell dynamics. Each equation describes the evolution of a sub-population, either proliferating or nonproliferating. The nonlinearity accounting for introduction of nonproliferating cells in the proliferating phase is assumed to depend upon the total number of cells. Existence and stability of steady states are investigated. A Lyapunov functional is built to obtain the global asymptotic stability of the...

Delay perturbed evolution problems involving time dependent subdifferential operators

Soumia Saïdi, Mustapha Fateh Yarou (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We investigate in the present paper, the existence and uniqueness of solutions for functional differential inclusions involving a subdifferential operator in the infinite dimensional setting. The perturbation which contains the delay is single-valued, separately measurable, and separately Lipschitz. We prove, without any compactness condition, that the problem has one and only one solution.

Delay-dependent asymptotic stability for neural networks with time-varying delays.

Liao, Xiaofeng, Yang, Xiaofan, Zhang, Wei (2006)

Discrete Dynamics in Nature and Society

Delay-dependent asymptotic stability of Cohen-Grossberg models with multiple time-varying delays.

Liao, Xiaofeng, Guo, Songtao (2007)

Discrete Dynamics in Nature and Society

Delay-dependent robust stability conditions and decay estimates for systems with input delays

Kostas Hrissagis, Olga I. Kosmidou (1998)

Kybernetika

The robust stabilization of uncertain systems with delays in the manipulated variables is considered in this paper. Sufficient conditions are derived that guarantee closed-loop stability under state-feedback control in the presence of nonlinear and/or time-varying perturbations. The stability conditions are given in terms of scalar inequalities and do not require the solution of Lyapunov or Riccati equations. Instead, induced norms and matrix measures are used to yield some easy to test robust stability...

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

This paper is devoted to the investigation on the stability for two characteristic functions $f_{1} (z) = z^{2} + p e^{- z τ} + q$ and $f_{2} (z) = z^{2} + p z e^{- z τ} + q$ , where $p$ and $q$ are real numbers and $τ > 0$ . The obtained theorems describe the explicit stability dependence on the changing delay $τ$ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Delay-dependent stability of high-order neutral systems

Yanbin Zhao, Guang-Da Hu (2021)

Kybernetika

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 of the...

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.

Deterministic minimax impulse control in finite horizon: the viscosity solution approach

Brahim El Asri (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We study here the impulse control minimax problem. We allow the cost functionals and dynamics to be unbounded and hence the value functions can possibly be unbounded. We prove that the value function of the problem is continuous. Moreover, the value function is characterized as the unique viscosity solution of an Isaacs quasi-variational inequality. This problem is in relation with an application in mathematical finance.

Differentiability of perturbed semigroups and delay semigroups

Charles J. K. Batty (2007)

Banach Center Publications

Suppose that A generates a C₀-semigroup T on a Banach space X. In 1953 R. S. Phillips showed that, for each bounded operator B on X, the perturbation A+B of A generates a C₀-semigroup on X, and he considered whether certain classes of semigroups are stable under such perturbations. This study was extended in 1968 by A. Pazy who identified a condition on the resolvent of A which is sufficient for the perturbed semigroups to be immediately differentiable. However, M. Renardy showed in 1995 that immediate...

Differentiable semiflows for differential equations with state-dependent delays.

Walther, Hans-Otto (2003)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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