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

• Published in: IEEE transactions on automatic control Vol. 67; no. 4; pp. 1685 - 1697
• Main Authors: Haidar, Ihab, Chitour, Yacine, Mason, Paolo, Sigalotti, Mario
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Asymptotic stability; Automatic; Control theory; Converse Lyapunov theorems; Dynamical systems; Engineering Sciences; exponential stability; infinite-dimensional systems; Mathematics; Nonlinear systems; Numerical stability; Optimization and Control; Stability analysis; Switching; Switching systems; Uncertainty; Infinite-dimensional systems; Switching systems; Exponential stability; Nonlinear systems; Converse Lyapunov theorems
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3080526

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 to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to uncertainties) local, semi-global, and global exponential stability, through the existence of coercive and non-coercive Lyapunov functionals. The importance of the obtained results is underlined through some applications concerning 1) exponential stability of nonlinear retarded systems with piecewise constant delays, 2) exponential stability preservation under sampling for semilinear control switching systems, and 3) the link between input-to-state stability and exponential stability of semilinear switching systems.