arXiv subjects

Mohamed Ali Hammami

Publications and source records attributed to Mohamed Ali Hammami.

3 recordsLinked to original sources

arXiv2025

Lyapunov methods for input-to-state stability of time-varying evolution equations

We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In particular, input-to-state stability of linear time-varying control systems in Hilbert spaces with bounded input operators is discussed. Methods for the construction of non-coercive LISS/iISS Lyapunov functions are presented for a certain class of time-varying semi-linear evolution equations. Two examples are given to illustrate the effectiveness of the results.

math.OC↗

arXiv2020

New results on the uniform exponential stability of non-autonomous perturbed dynamical systems

In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates on the perturbation terms, the equilibrium point remains (globally) uniformly exponentially stable. The results we obtained can easily be applied in practice since they are based on the Gronwall-Bellman inequalities rather than the classical Lyapunov methods that require the knowledge of a Lyapunov function. Several numerical examples are presented in order to illustrate the validity of our study, especially when the standard Lyapunov approaches are useless.

math.DS↗

arXiv2015

On the practical global uniform asymptotic stability of stochastic differential equations

The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of so- lutions of stochastic differential equations based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.

math.AP↗