Stabilization of Crystallization Models Governed by Hyperbolic Systems

TL;DR

This paper introduces a control design method using Lyapunov functionals to stabilize steady-state solutions in hyperbolic PDE models of continuous crystallization, ensuring exponential stability.

Contribution

It develops a novel control approach based on quadratic Lyapunov functionals for stabilizing hyperbolic systems modeling crystallization processes.

Findings

Guarantees exponential stability of the controlled system.

Provides a systematic method for constructing control Lyapunov functionals.

Applicable to models with constant inputs and steady-state solutions.

Abstract

This paper deals with mathematical models of continuous crystallization described by hyperbolic systems of partial differential equations coupled with ordinary and integro-differential equations. The considered systems admit nonzero steady-state solutions with constant inputs. To stabilize these solutions, we present an approach for constructing control Lyapunov functionals based on quadratic forms in weighted L2-spaces. It is shown that the proposed control design scheme guarantees exponential stability of the closed-loop system.