Input-to-State Stability of time-varying infinite-dimensional control systems

TL;DR

This paper extends the input-to-state stability (ISS) concept to time-varying infinite-dimensional control systems, providing a framework for analyzing robustness in complex PDE-based models.

Contribution

It develops new ISS criteria and Lyapunov methods tailored for time-varying infinite-dimensional systems, advancing the robustness analysis of PDE control systems.

Findings

Established ISS conditions for time-varying infinite-dimensional systems

Developed Lyapunov-based stability criteria for PDE control

Applied results to robust stabilization of specific PDE models

Abstract

The concept of input-to-state stability (ISS) proposed in the late 1980s is one of the central notions in robust nonlinear control. ISS has become indispensable for various branches of nonlinear systems theory, such as robust stabilization of nonlinear systems, design of nonlinear observers, analysis of large-scale networks, etc. The success of the ISS theory of ODEs and the need for robust stability analysis of partial differential equations (PDEs) motivated the development of ISS theory in the infinite-dimensional setting. For instance, the Lyapunov method for analysis of iISS of nonlinear parabolic equations. For an overview of the ISS theory for distributed parameter systems. ISS of control systems with application to robust global stabilization of the chemostat has been studied with the help of vector Lyapunov functions.