Lyapunov exponents of a dynamical system give information about its long-term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In a previous paper, the authors proposed an algorithm for Lyapunov exponents estimation in piecewise linear systems that strongly reduces the computational time. ...

We study the stability properties of a class of time-varying nonlinear systems. We assume that nonstrict input-to-state stable (ISS) Lyapunov functions for our systems are given. We posit a mild nondegeneracy condition on our given Lyapunov functions under which strict ISS Lyapunov functions for our systems are also known to exist. However, the known existence result is based on value function ...

Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established.

We investigate the statistical properties of local Lyapunov exponents which characterize magnon localization in the one-dimensional Heisenberg-Mattis spin glass HMSG at zero temperature by means of a connection to a suitable version of the Fokker-Planck FP equation. We consider the local Lyapunov exponents LLEs , in particular, the case of instantaneous LLE. We establish a connection between th...

New bounds for solutions of the discrete algebraic Lyapunov equation P = APA T + Q are derived. The new bounds are compared to existing ones and found to be of particular interest when A is non-normal.

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

The problem of robust output-feedback control for a class of uncertain switching fuzzy control systems is investigated. Asymptotic stability of the observer, based on the error equation, is obtained by using the switching technique and the common Lyapunov function method. Switching laws are also designed via using single Lyapunov function method for observer equation such that the closed-loop s...

This article studies stabilisation problem for time-varying linear systems via state feedback. Two types of controllers are designed by utilising solutions to Lyapunov differential equations. The first type of feedback controllers involves the unique positive-definite solution to a parametric Lyapunov differential equation, which can be solved when either the state transition matrix of the open...

We consider the trajectories of particles suspended in a randomly moving fluid. If the Lyapunov exponent of these trajectories is negative, the paths of these particles coalesce, so that particles aggregate. Here we give a detailed account of a method [B. Mehlig and M. Wilkinson, Phys. Rev. Lett. 92, 250602 (2004)] for calculating this exponent: it is expressed as the expectation value of a ran...

We calculate the Lyapunov exponents in a classical molecular dynamics framework. Yukawa and Slater-Kirkwood forces are considered in order to give an equation of state that resembles the nuclear and the atomic He equation of state, respectively, near the critical point for liquid-gas phase transition. The largest Lyapunov exponents l are always positive and can be very well fitted near the “cri...