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Conditions for the Uniform Asymptotic Stability of Delay Differential Equations
Differential Equations, 2001The following system of functional-differential equations with delay \[ \frac{dx(t)}{dt}=f(t,x_t),\quad f(t,0)\equiv 0, \tag{1} \] is considered, and the asymptotic stability of its solution \[ x(t)\equiv 0\tag{2} \] is studied. Let \(a, b\), and \(\omega\) be functions of Hahn's class, and let \(p: \mathbb{R}_+\to \mathbb{R}_+\) be a function ...
Knyazhishche, L. B., Shcheglov, V. A.
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Ukrainian Mathematical Journal, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammed, S. A., Tunc, C.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mohammed, S. A., Tunc, C.
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On the Global Uniform Asymptotic Stability of Time-Varying Systems
Differential Equations and Dynamical Systems, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Damak, H., Hammami, M. A., Kalitine, B.
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Uniform Asymptotic Stability and Slow Convergence in Adaptive Systems
IFAC Proceedings Volumes, 2013Abstract We examine convergence properties of errors in a class of adaptive systems that arises for scalar plants. We show that these adaptive systems are at best uniformly asymptotically stable in the large, and possess an infinite region where the trajectories move arbitrarily slowly, i.e. stick.
Benjamin Jenkins +3 more
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Global uniform asymptotic stabilization of an underactuated surface vessel
IEEE Transactions on Automatic Control, 2002Explicit formulas of smooth time-varying state feedbacks which make the origin of an underactuated surface vessel globally uniformly asymptotically stable are proposed. The construction of the feedback extensively relies on the backstepping approach. The feedbacks constructed are time periodic functions.
Frédéric Mazenc +2 more
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On uniform asymptotic stability of nonlinear Volterra integro-differential equations
International Journal of Control, 2020Using a novel approach, we present some new scalar criteria for the uniform asymptotic stability of general nonlinear Volterra integro-differential equations.
Pham Huu Anh Ngoc, Le Trung Hieu
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Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space
SIAM Journal on Mathematical Analysis, 1972This paper contains two major results. The first one is to obtain necessary and sufficient conditions for the uniform asymptotic stability of linear evolutionary processes which are defined in a general Banach space and whose norms can increase no faster than an exponential. This is the substance of Theorem 1 and its corollaries.
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Uniform Asymptotic Stabilization of Affine Periodic Discrete-Time Systems
2020 59th IEEE Conference on Decision and Control (CDC), 2020In this article, we study the problem of asymptotic stabilization for nonlinear affine discrete-time control systems with periodic coefficients via state feedback. It is supposed that the origin of the free dynamic system is (non-asymptotically) stable.
Adam Czornik +4 more
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Funkcialaj Ekvacioj, 1997
The purpose of this paper is to improve the results by the use of Lyapunov functionals on stability as well as on boundedness for a system of differential equations \(x'=F(t,x_t)\) with constant delay \(h>0\). The improvement is to extend the more general form by the use of the convexity of a wedge.
Kobayashi, Katsumasa, Tsuruta, Kunio
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The purpose of this paper is to improve the results by the use of Lyapunov functionals on stability as well as on boundedness for a system of differential equations \(x'=F(t,x_t)\) with constant delay \(h>0\). The improvement is to extend the more general form by the use of the convexity of a wedge.
Kobayashi, Katsumasa, Tsuruta, Kunio
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Uniform Asymptotic Stability by Indefinite Lyapunov Functions
2022 13th Asian Control Conference (ASCC), 2022Gökhan Sahan, Derya Özdemir
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