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.
Rigorous global asymptotic stability
of the system was established.
In ,  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