Controllability and Stabilization of a Wave-Heat Cascade System

TL;DR

This paper investigates the controllability and stabilization of a coupled wave-heat PDE system, introducing new control strategies and proving controllability via observability inequalities, with the operator being a Riesz-spectral operator.

Contribution

It establishes controllability results for a wave-heat cascade system using an Ingham-M{"u}ntz inequality and designs an explicit output feedback control for stabilization.

Findings

Controllability achieved through observability inequalities.

Explicit feedback control stabilizes the PDE cascade.

Operator identified as Riesz-spectral, aiding control design.

Abstract

Considering a wave-reaction-diffusion PDE cascade system with wave Neumann control, we first establish controllability properties in a suitable Hilbert space depending on the coupling cascade term. This is done by deriving an observability inequality for the dual problem by resorting to an Ingham-M{\"u}ntz inequality. Second, we design an explicit output feedback control strategy for the actual stabilization of the PDE cascade. The key property is that the underlying operator is a Riesz-spectral operator.