Exponential stability of discrete linear repetitive processes

Guaranteed cost control for uncertain 2-D discrete systems with state delay in the Roesser model

“…Many physical processes, such as image processing [4], signal filtering [5], and thermal processes in chemical reactors, heat exchangers and pipe furnaces [3], have a clear 2-D structure. The 2-D system theory is frequently used as an analysis tool to solve some problems, e.g., iterative learning control [6][7] and repetitive process control [8][9]. However, the analysis and synthesis approaches for 2-D systems can not simply extend from existing standard (1-D) system techniques because there are many 2-D system phenomena which have no I-D system counterparts.…”

Exponential stability conditions for 2D continuous state-delayed systems

“…[15], [19], [10]) except for a few recent papers that inspired our work [1], [9] where a Lyapunov approach is applied to continuous Roesser model. As for exponential stability, to the authors knowledge, only two papers ( [13] and [4]) have been devoted to this form of stability for 2D systems both showing that exponential stability is equivalent to asymptotic stability which is not surprising in the linear case. But the study of exponential stability is still important as it guarantees a decay Mariem.Ghamgui@etu.univ-poitiers.fr, Nima.Yeganefar@univ-poitiers.fr, Olivier.Bachelier@univ-poitiers.fr, Driss.Mehdi@univ-poitiers.fr rate where asymptotic stability does not.…”

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

“…One of the only works dealing with this problem is given by Pandolfi in [4]. Later in [23], the authors extended this definition to repetitive systems but we are not discussing this special type of multidimensional systems in this technical note. It is interesting to point out that Pandolfi takes the initial conditions on the positive semi-axes and proposes the following definition: the equilibrium point is exponentially stable if there exists a constant such that for some , all trajectories satisfy:…”