Exponential Stability of a Class of Infinite Dimensional Coupled Systems

TL;DR

This paper investigates the exponential stability of infinite dimensional coupled systems, proving conditions under which the coupled system inherits stability from its subsystems, with applications to control theory.

Contribution

It establishes admissibility conditions ensuring the coupled system is governed by a $C_0$-semigroup and inherits exponential stability from stable subsystems.

Findings

Coupled systems are governed by $C_0$-semigroups under certain conditions.

Exponential stability of subsystems implies stability of the coupled system.

Simplified proofs for semigroup generation and stability in control systems.

Abstract

This paper is concerned with exponential stability of a class of infinite dimensional coupled systems. It is proved that under some admissibility conditions, the considered infinite dimensional coupled system is governed by a $C_0$-semigroup. Furthermore, if both the free subsystems are governed by exponentially stable $C_0$-semigroups, then so is the coupled system. The results are applied to simplify the proof of semigroup generation and exponential stability for several coupled systems emerged in control theory literatures.