Necessary and sufficient conditions for exponential stabilization of systems affine in controls

TL;DR

This paper establishes exact conditions for the exponential stabilization of distributed affine control systems in Banach spaces using constant controls, including explicit convergence rate estimates and practical applications.

Contribution

It provides the first complete set of necessary and sufficient conditions for stabilization of such systems with explicit convergence estimates.

Findings

Derived explicit convergence speed estimates.

Established necessary and sufficient conditions for stabilization.

Demonstrated applications in distributed control systems.

Abstract

This paper provides necessary and sufficient conditions for exponential stabilization of distributed systems affine in control, evolving in a Banach state space, by means of constant controls. An explicit estimate of the convergence speed is obtained under the given constant control. Various applications are provided.