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 ?
Among the research topics are the hypergroupoid of boundary conditions for local quantum observables, the asymptotic stability of connective groups, the K-theory of the flip automorphisms, the modular cocycle from commensuration and its Mackey range, and the classification of gapped Hamiltonians in quantum spin chains.
We determined the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems.
With the help of Lemma 6, we obtain the following theorem when [theta] [member of] [0, 1/2), which offers a sufficient and necessary condition of asymptotic stability for the linear [theta]-method.
In this paper, in comparison to the existing works, a novel framework and a methodology are provided where model reference and Lyapunov-based adaptive control methodology (based on the thesis work of Lu [20]) is implemented to aid such a damaged aircraft to land safely, with provided asymptotic stability guarantees.
This technique, known as the perturbation method (see [2]), has many applications in the theory of fractional differentiation operators (see [3]), in reaction-diffusion equations, stochastic stability, and asymptotic stability (see [4-9]), and for some numerical considerations (see, for example, [10-12]).
The position and force control task presented in [43] has been defined considering the manipulator and environment models; asymptotic stability of the control systems is demonstrated, and experimental study of the issue is presented.
Dhage, "Global asymptotic stability of solutions of a functional integral equation," Nonlinear Analysis: Theory, Methods & Applications, vol.
A nonlinear backstepping controller is designed in Section 4, and the analysis of global asymptotic stability using Lyapunov stability criteria is given in the same section.
(2) weak asymptotic stability in probability is equivalent to the [M.sup.[gamma].sub.0]-stability for some y satisfying Property [gamma]1;
To the best of our knowledge from the literature, we did not find any paper on the existence of periodic solutions, stability, asymptotic stability, square integrability, and boundedness of solutions of a mathematical model like (13).
Asymptotic stability analysis of non-autonomous systems is generally much harder than that of autonomous systems, since it is usually very difficult to build a Lyapunov function with a negative definite derivative.
On the other hand, it is desirable to understand the asymptotic behavior of the quasi-geostrophic equation, especially for the asymptotic stability of solutions.

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