Input-to-state stability of infinite-dimensional systems: Foundations and present-day developments
Andrii Mironchenko, Christophe Prieur (GIPSA-INFINITY)
TL;DR
This paper reviews the foundational aspects of input-to-state stability (ISS) in infinite-dimensional systems, emphasizing Lyapunov methods, applications, and a small-gain theorem for interconnected systems.
Contribution
It provides a comprehensive overview of ISS theory in infinite-dimensional systems, highlighting recent developments and Lyapunov-based stability analysis techniques.
Findings
Fundamental facts of infinite-dimensional ISS theory summarized.
Application of Lyapunov methods to various classes of systems.
A Lyapunov-based small-gain theorem for interconnected ISS systems.
Abstract
Input-to-state stability (ISS) unifies the stability and robustness in one notion, and serves as a basis for broad areas of nonlinear control theory. In this contribution, we covered the most fundamental facts in the infinite-dimensional ISS theory with a stress on Lyapunov methods. We consider various applications given by different classes of infinite-dimensional systems. Finally, we discuss a Lyapunov-based small-gain theorem for stability analysis of an interconnection of two ISS systems.
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