Related papers: Almost Lyapunov Functions for Nonlinear Systems
We study the quasi-stationary behavior of multidimensional processes absorbed when one of the coordinates vanishes. Our results cover competitive or weakly cooperative Lotka-Volterra birth and death processes and Feller diffusions with…
We prove that the Lyapunov exponents, cosidered as functions of measures with non compact support, are semicontinuous with respect to the Wasserstein topology but not with respect to the weak* topology. Moreover, we prove that they are not…
We use the uniform semiclassical approximation in order to derive the fidelity decay in the regime of large perturbations. Numerical computations are presented which agree with our theoretical predictions. Moreover, our theory allows to…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
We address the problem of designing an observer for triangular non locally Lipschitz dynamical systems. We show the convergence with an arbitrary small error of the classical high gain observer in presence of nonlinearities verifying some…
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
In this paper, we study the construction of Lyapunov functions based on first order approximations. In a first part, the study of local exponential stability property of a transverse invariant manifold is considered. This part is mainly a…
We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semi-groups. When not checkable on the whole state space, it can be combined to the use of…
We consider here the dynamics of some homogeneous and isotropic cosmological models with $N$ interacting classical scalar fields non-minimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
A mathematical model of autoresonance in nonlinear systems with combined parametric and external chirped frequency excitation is considered. Solutions with a growing amplitude and a bounded phase mismatch are associated with the…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an…
We study the regularity of Lyapunov exponents as functions on the space of compactly supported probability measures on $\mathrm{GL}(d,\mathbb{R})$. We prove that the Lyapunov exponents are pointwise log-H\"older continuous with respect to…
In this paper, we consider a linear fractional differential equation with fractional boundary conditions. First, by obtaining Green's function, we derive the Lyapunov-type inequalities for such boundary value problems. Furthermore, we use…
We study the asymptotic stability properties of nonlinear switched systems under the assumption of the existence of a common weak Lyapunov function. We consider the class of nonchaotic inputs, which generalize the different notions of…
This SSFG Lp stability theorem can predict permissible forcing amplitudes below which a finite nonlinear input-output gain can be maintained. Our analysis employs Linear Matrix Inequalities (LMI) and Sum-of-Squares (SOS) as the primary…