Results 191 to 200 of about 14,104 (237)

Some Refinements of Lyapunov's Second Method

Canadian Journal of Mathematics, 1965
Lyapunov's second method is a well-known and powerful tool for studying the behaviour of solutions of a system of differential equations. One approach to the theory is the comparison method developed by Corduneanu (4). This approach has the advantage that it also leads to other results on asymptotic behaviour which originally appeared to be unrelated ...
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A Lyapunov analysis of accelerated methods in optimization

J. Mach. Learn. Res., 2021
Summary: Accelerated optimization methods, such as Nesterov's accelerated gradient method, play a significant role in optimization. Several accelerated methods are provably optimal under standard oracle models. Such optimality results are obtained using a technique known as ``estimate sequences,'' which yields upper bounds on convergence properties ...
Ashia C. Wilson, Ben Recht, Michael I. Jordan   +2 more
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Suppressing chaos via Lyapunov–Krasovskii’s method

Chaos, Solitons & Fractals, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kuang, JL, Meehan, PA, Leung, AYT
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Method of Lyapunov Functions

2020
The celebrated Lyapunov function method (or the direct Lyapunov method) introduced in the Ph.D. thesis of A. M. Lyapunov in 1892 is a simple effective tool for stability analysis of differential equations. The main advantage of this method lies in the fact that a decision on stability or instability can be made by means of a certain investigation of ...
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On the lyapunov's functionals method for systems with delays

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author analyzes various derivatives of functionals, needed to use Lyapunov theory. In particular, the notions (too lengthy to be quoted here) of invariant continuity and invariant differentiability are introduced. For the proofs of the few results given, the reader is referred elsewhere.
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The Direct Method of Lyapunov

1987
Let us consider a problem of mechanics defined by the system of ordinary differential equations (1.5.1) and let us investigate the stability of a particular solution q i 0 (t). For purposes of simplicity, we have omitted the influence of any parameters. The following variational equations are obtained by the well-known transformation (1.2) q
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The status of synthesis using Lyapunov's method

Automatica, 1965
This paper surveys the literature devoted to techniques for the synthesis of control systems based on Lyapunov's second method. The work is tutorial in nature and attempts to unify some of the scattered literature on the subject. A number of techniques are reviewed, illustrated with examples, and comments made regarding their applicability and ...
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The Lyapunov Function Method

1999
In Chapter 7 we discussed the first approach to realization of the Lyapunov direct method for FDE based on application of the Lyapunov functionals. In the second approach finite dimensional Lyapunov’s functions v(t, x): R × R n →R are used.
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The Method of Lyapunov Functions: RNNs

2013
In this chapter, we apply the method of Lyapunov functions for differential equations with piecewise constant argument of generalized type to a model of RNNs. The model involves alternating argument. Sufficient conditions are obtained for global exponential stability of the equilibrium point.
Marat Akhmet, Enes Yılmaz
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The Lyapunov–Razumikhin Method: CNNs

2013
In this chapter, by using the concept of differential equations with piecewise constant arguments of generalized type [13–15, 18], the model of cellular neural networks (CNNs) [79, 80] is developed. Lyapunov–Razumikhin technique is applied to find sufficient conditions for uniform asymptotic stability of equilibria.
Marat Akhmet, Enes Yılmaz
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