Mariem Ghamgui

Lyapunov Theory for 2-D Nonlinear Roesser Models: Application to Asymptotic and Exponential Stability

This technical note deals with a general class of discrete 2-D possibly nonlinear systems based on the Roesser model. We first motivate the introduction of Lyapunov type definitions of asymptotic and exponential stability. This will allow us to introduce and discuss several particularities that cannot be found in 1-D systems. Once this background has been carefully designed, we develop different Lyapunov theorems in order to check asymptotic and exponential stability of nonlinear 2-D systems. Finally we propose the first converse Lyapunov theorem in the case of exponential stability.

Robust stability of hybrid Roesser models against parametric uncertainty: a general approach

This paper aims at proposing a general framework for the establishement of LMI conditions to analyse the robust stability of a singular hybrid Roesser model subject to parametric uncertainties. The uncertain parameters are involved through implicit Linear Fractional Representations (LFR). Special focus is put on the influence of the number of uncertain parameters and the dimensionality of the model. More precisely it is shown that each dimension can nearly be regarded as an uncertain parameter and the other way around. Therefore, their influence on the conservatism of the obtained condition is very similar.

H ∞ Performance Analysis of 2D Continuous Time-Varying Delay Systems

This paper deals with the problem of

Stability and stabilization of 2D continuous state-delayed systems

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S-procedure for deriving stability conditions of hybrid Roesser models

H∞ performance analysis of 2D continuous time-varying delay systems described by Roesser model. Using a simple Lyapunov–Krasovskii functional, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities. The obtained result is then extended to the problem of

On the robust state-feedback stabilisation of nD hybrid Roesser models with implicit LFR uncertainty

H_{\infty }