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Asymptotic Stability of Fractional Langevin Systems
Journal of Applied Nonlinear Dynamics, 2022Summary: In the paper, we present a method based on eigenvalue criterion to test the asymptotic stability of fractional linear Langevin systems represented by the fractional differential equation in the sense of Caputo fractional derivative. Also, this method is extended to nonlinear equations and finally some sufficient conditions ensuring ...
Govindaraj, Venkatesan +3 more
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Stability and Asymptotic Stability of Functional-Differential Equations
Journal of the London Mathematical Society, 1995For 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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2014
A class of abstract dynamical systems with multivalued flows of solutions in a metric space is introduced in this chapter. For this class of systems, the property of partial asymptotic stability with respect to a continuous functional is studied. In order to characterize the limit set of a trajectory of a multivalued system, a modification of the ...
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A class of abstract dynamical systems with multivalued flows of solutions in a metric space is introduced in this chapter. For this class of systems, the property of partial asymptotic stability with respect to a continuous functional is studied. In order to characterize the limit set of a trajectory of a multivalued system, a modification of the ...
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Optimisation and asymptotic stability
International Journal of Control, 2016ABSTRACTThe 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 ...
B. T. Polyak, P. S. Shcherbakov
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Invariance and asymptotic stability
Journal of Applied Mathematics and Mechanics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stability and Asymptotic Behaviour
2014The focus of this chapter is threefold in theme. Firstly, the topic of stability of equilibria will be investigated in the context of an autonomous differential equation \( \dot{x} = f\left( x \right) \) with an equilibrium at 0 (i.e. f(0) = 0). Loosely speaking, this topic addresses the following question: in forwards time, do solutions which start ...
Hartmut Logemann, Eugene P. Ryan
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Asymptotic Stability for Nonlinear Parabolic Systems
1996The problem of asymptotic stability for second order ordinary differential equations is well-known in the literature. Recently, various extensions of this work have been given for the case of second order hyperbolic systems (see [1–5]). On the other hand, the situation for parabolic systems has received much less discussion, so that a study of this ...
PUCCI, Patrizia, J. SERRIN
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Intrinsic robustness of global asymptotic stability
Systems & Control Letters, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stability and Asymptotic Behavior
1998We resume the problems treated in §12. In contrast to the case investigated there, we now consider solutions defined on infinite intervals. In this setting, continuous dependence on initial conditions and on the right side of the differential equation is a significantly more complicated matter than in §12, where general results were obtained under ...
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