Lyapunov Characterization of Uniform Exponential Stability for Nonlinear Infinite-Dimensional Systems

In this article, we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to uncertainties. We first extend the well-known Datko lemma framework of considered class systems. Thanks generalization, provide characterizations uniform (with respect uncertainties) local, semi-global, and global exponential stability, through existence coercive non-coercive Lyapunov functionals. The importance obtained results is underlined some applications concerning 1) stability retarded piecewise constant delays, 2) preservation under sampling for semilinear control switching systems, 3) link between input-to-state