Displaying similar documents to “Robustness with respect to small time-varied delay for linear dynamical systems on Banach spaces”

On delay-dependent stability for neutral delay-differential systems

Qing-Long Han (2001)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.

Stabilization of solutions to a differential-delay equation in a Banach space

J. J. Koliha, Ivan Straškraba (1997)

Annales Polonici Mathematici

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A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.

On delay-dependent robust stability under model transformation of some neutral systems

Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)

Kybernetika

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This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust...

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...

An analysis on the stability of a state dependent delay differential equation

Sertaç Erman, Ali Demir (2016)

Open Mathematics

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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t). τ ( u ( t ) ) = a + b u ( t ) c + b u ( t ) . Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

Pin-Lin Liu (2005)

International Journal of Applied Mathematics and Computer Science

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This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

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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.