Results 21 to 30 of about 9,796 (225)
Sample path properties of the stochastic flows [PDF]
, 2004 We consider a stochastic flow driven by a finite-dimensional Brownian motion. We show that almost every realization of such a flow exhibits strong statistical properties such as the exponential convergence of an initial measure to the equilibrium state ...
Dolgopyat, Dmitry +2 more
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Feedback Stabilization and Lyapunov Functions [PDF]
SIAM Journal on Control and Optimization, 2000 The authors consider the problem of finding a feedback stabilizing law \(x \to k(x)\) associated with a control system \(x'(t) = f(x(t),u(t))\). Using the concept of positional strategies introduced in the framework of differential games by Krasovskii and Subbotin in 1988, assuming the existence of a Lyapunov Lipschitz function \(V\) defined on the ...
Francis H. Clarke +3 more
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A discrete logarithmic function and Lyapunov function
JSIAM Letters, 2022 Summary: The Lyapunov function plays an important role in the stability theory of dynamical systems. Its counterpart for discrete dynamical systems is not studied so much, though importance of such systems is increasing. In this letter, an attempt is made to construct a discrete analog of the Lyapunov function for the competitive Lotka-Volterra ...
Shin Isojima, Seiichiro Suzuki
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Computation and Verification of Lyapunov Functions [PDF]
SIAM Journal on Applied Dynamical Systems, 2015 Summary: Lyapunov functions are an important tool to determine the basin of attraction of equilibria in Dynamical Systems through their sublevel sets. Recently, several numerical construction methods for Lyapunov functions have been proposed, among them the RBF (Radial Basis Function) and CPA (Continuous Piecewise Affine) methods.
Peter Giesl, Sigurdur F. Hafstein
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Nonautonomous Dynamical Systems, 2016 In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10]
Raffoul Youssef, Rai Habib
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On Vector Lyapunov Functions [PDF]
Proceedings of the American Mathematical Society, 1971 It has been proved that the use of a vector Lyapunov function is more advantageous in certain situations rather than a scalar function. Moreover, each function needs to satisfy less rigid requirements. In this paper a new situation has been considered where vector Lyapunov functions play a further useful role. For this purpose, a new type of stability,
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Learning lyapunov functions for hybrid systems [PDF]
Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control, 2021 We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop dynamics of linear systems with model predictive controllers, piecewise affine/linear complementarity/mixed-logical ...
Shaoru Chen +4 more
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Some stability and boundedness criteria for a class of Volterra integro-differential systems
Electronic Journal of Qualitative Theory of Differential Equations, 2002 Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations.
Jito Vanualailai
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Review on the Stability of the Peregrine and Related Breathers
Frontiers in Physics, 2020 In this note, we review stability properties in energy spaces of three important nonlinear Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev.
Miguel A. Alejo +2 more
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Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application [PDF]
, 2015 With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined.
Chernyshenko, SI +5 more
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