相关论文: Almost Global Stochastic Stability
Suppose that the origin is globally asymptotically stable under a set of continuous vector fields on Euclidean space and suppose that all those vector fields come equipped with -- possibly different -- convex Lyapunov functions. We show…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
We use the semi-discrete method, originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6), to reproduce qualitative…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the…
We establish metastability in the sense of Lebowitz and Penrose under practical and simple hypothesis for (families of) Markov chains on finite configuration space in some asymptotic regime, including the case of configuration space size…
We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant…
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…
This paper proposes a notion of viscosity weak supersolutions to build a bridge between stochastic Lyapunov stability theory and viscosity solution theory. Different from ordinary differential equations, stochastic differential equations…
This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
In this paper we show that uniformly global asymptotic stability for a family of ordinary differential equations is equivalent to uniformly global exponential stability under a suitable nonlinear change of variables. The same is shown for…
We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone…
The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under any $L^2$-perturbation. In particular the general hypothesis…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…