On Hyperexponential Stabilization of Linear Infinite-Dimensional Systems

TL;DR

This paper introduces a method for hyperexponential stabilization of infinite-dimensional systems on Hilbert spaces using distributed, time-dependent control laws, ensuring stability and input-to-state stability through Lyapunov analysis.

Contribution

It develops a novel approach for stabilizing infinite-dimensional systems with time-dependent controls and proves stability properties using Lyapunov methods and operator theory.

Findings

Established well-posedness of the closed-loop system for all times

Proved hyperexponential stability of the controlled system

Demonstrated input-to-state stability under the proposed control law

Abstract

This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal monotone operator. The hyperexponential stability and ISS property of the closed loop is established using Lyapunov analysis and time scale transformation.