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On Criteria for Asymptotic Stability

Russian Mathematics, 2022
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Optimisation and asymptotic stability

International Journal of Control, 2016
ABSTRACTThe problems of unconstrained optimisation and establishing asymptotic stability have much in common. Understanding the analogy between these two sheds light on their interconnection and may lead to a number of new results. For instance, in this paper, we provide estimates of the rate of convergence when analysing asymptotic stability of ...
Boris T. Polyak   +1 more
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Stability and Asymptotic Stability for Subcritical gKdV Equations

Communications in Mathematical Physics, 2002
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Yvan Martel, Tai-Peng Tsai, Frank Merle
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Liapunov asymptotic stability and Zhukovskij asymptotic stability

Chaos, Solitons & Fractals, 2000
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On asymptotic stabilization of driftless systems

Applied Mathematics and Computation, 2000
The authors consider the problem of stabilizing the driftless system \[ \dot{x} = g(x)u(t) \] by the state feedback \(u=u(x)\). Instead of a control Lyapunov function, the authors adopt an approach based on expansions which are similar to the first method of Lyapunov.
Yew-Wen Liang, Der-Cherng Liaw
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On the Poincaré Criterion for Asymptotic Stability

SIAM Journal on Mathematical Analysis, 1979
This work discusses an n dimensional generalization of the Poincare criterion for asymptotic stability of a periodic solution to an ordinary differential equation. We define a function along a trajectory which measures the projection, normal to the flow, of a solution to the linearized equations. When this function satisfies certain monotone conditions,
Churchill, R. C., Selgrade, J. F.
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Asymptotic Stability in an Epidemic System

Mathematical Methods in the Applied Sciences, 1996
Summary: Using the invariance principle in Banach space with less restrictions, we discuss the asymptotic behaviour of an integro-differential equation with infinite delay which is an infectious disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kernel satisfies a ...
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Stability and Asymptotic Stability of Functional-Differential Equations

Journal of the London Mathematical Society, 1995
For the scalar equation \[ y'(t)= a(t) y(t)+ b(t) y(\theta(t))+ c(t) y'(\theta(t)),\;y(0)= y_0, \] where (i) the lag function \(\theta\) is nonnegative and continuous, \(\theta(t)\leq t\) for \(t\geq 0\), (ii) the complex functions \(a\), \(b\), \(c\) reside in \(C[0, \infty)\), (iii) \(\alpha(t):= \text{Re } a(t)\leq 0\), \(|c(t)|\leq c^*< 1\), \(t ...
Iserles, Arieh, Terjéki, József
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