Related papers: On the Stability Functional for Conservation Laws
We introduce the matching functions technique in the setting of Anosov flows. Then we observe that simple periodic cycle functionals (also known as temporal distance functions) provide a source of matching functions for conjugate Anosov…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an invariant…
This paper is concerned with the stability of stationary solutions of the conservation law $\partial_t u + \mathrm{div}_y A(y,u) -\Delta_y u=0$, where the flux $A$ is periodic with respect to its first variable. Essentially two kinds of…
We prove global existence, uniqueness and $\L1$ stability of solutions to general systems of nonlocal conservation laws modeling multiclass vehicular traffic. Each class follows its own speed law and has specific effects on the other…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
We obtain a Liouville property for stationary diffusions in random environment which are small, isotropic perturbations of Brownian motion in spacial dimension greater than two. Precisely, we prove that, on a subset of full probability, the…
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…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear…
In this paper we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural…
We study the long-time behavior of almost periodic solutions to stochastic scalar conservation laws in any space dimension, under the assumption of Lipschitz continuity of the flux functions and a non-degeneracy condition. We show the…
In the previous paper \cite{J1}, we established pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves $\bar u$ of a system of reaction diffusion equations, and also obtained…
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…
Consider a symmetric $\alpha$-stable L\'evy process with $\alpha\in (1,2)$. We study shifted small ball probabilities for these processes in the uniform topology, when the shift function is an arbitrary continuous function which starts at…
A new functional-based approach is developed for the stability analysis of linear impulsive systems. The new method, which introduces looped-functionals, considers non-monotonic Lyapunov functions and leads to LMIs conditions devoid of…
The property that a one to one function from the natural numbers to itself preserves the density of sub-sets is shown to be equivalent to a condition on the covering of intervals in the range of the function by images of intervals in the…
In this note, we propose coordinate-invariant notions of incremental Lyapunov function and provide characterizations of incremental stability in terms of existence of the proposed Lyapunov functions.
We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition…