On partial stability for delay systems
C. Corduneanu (1975)
Annales Polonici Mathematici
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Displaying similar documents to “An analysis on the stability of a state dependent delay differential equation”
On partial stability for delay systems
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.
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...
On stability of linear neutral differential equations with variable delays
Leonid Berezansky, Elena Braverman (2019)
Czechoslovak Mathematical Journal
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We present a review of known stability tests and new explicit exponential stability conditions for the linear scalar neutral equation with two delays where and for its generalizations, including equations with more than two delays, integro-differential equations and equations with a distributed delay.
Robustness with respect to small time-varied delay for linear dynamical systems on Banach spaces
Miao Li, Xiao-Hui Gu, Fa-Lun Huang (2004)
Studia Mathematica
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Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.
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.
Stability and Boundedness of Solutions of a Certain System of Third-order Nonlinear Delay Differential Equations
Mathew Omonigho Omeike (2015)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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In this paper a number of known results on the stability and boundedness of solutions of some scalar third-order nonlinear delay differential equations are extended to some vector third-order nonlinear delay differential equations.
Characterization of shadowing for linear autonomous delay differential equations
Mihály Pituk, John Ioannis Stavroulakis (2025)
Czechoslovak Mathematical Journal
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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.
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.