asymptotic stability


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asymptotic stability

[ā‚sim′täd·ik stə′bil·əd·ē]
(mathematics)
The property of a vector differential equation which satisfies the conditions that (1) whenever the magnitude of the initial condition is sufficiently small, small perturbations in the initial condition produce small perturbations in the solution; and (2) there is a domain of attraction such that whenever the initial condition belongs to this domain the solution approaches zero at large times.
References in periodicals archive ?
1) including their boundedness, integrability, and the stability and global asymptotic stability of the zero solution.
About 260 papers consider such topics as analyzing the traffic and user behavior of online mobile games, modeling and simulating a ship's fuel supply unit, the asymptotic stability of a system with two identical robots and a built-in safety, using Wikipedia categories for discovering the themes of text documents, the behavior evolution of a duffing oscillator, an active contour model based on local and global image information, an aged-care service information system based on cloud computing, and automobile anti-collision millimeter-wave radar signal processing.
In [7], [8] the authors claimed that asymptotic stability is direct a consequence of Mittag-Leffler stability, but they did not present any proof of this statement.
In this section we establish a test for the asymptotic stability of the system (1) equilibrium when D is an open subset of
This section is concerned in determine a condition so that the closed-loop system presented in Equation (8) is asymptotically stable in the Lyapunov sense, on this account Lyapunov stability theorems give sufficient conditions for stability and asymptotic stability (SHUSHI et al.
Schlage-Puchta, Asymptotic stability for sets of polynomials, Arch.
Among the topics are the lower Perron exponent and its properties, Millionschikov's method of rotation and the attainability of central and exponential exponents and their instability, Lyapunov transformations, linear systems under exponentially decreasing perturbations, and asymptotic stability by linear approximation.
In Sections 4 and 5, we show that the global asymptotic stability of these equilibria depend only on the basic reproduction numbers under some hypotheses on the incidence function.
Lyapunov second method enables to consider the stability or the asymptotic stability in a certain area Q, in general with the linear or nonlinear system, (of both excited and unexcited system).
By using parameter-dependent Lyapunov functionals, some less conservative results for asymptotic stability of uncertain polytopic delay systems have been proposed in [3, 12, 15, 20] via LMIs.
But it is necessary to guarantee the global asymptotic stability.

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