Integral action feedback design for conservative abstract systems in the presence of input nonlinearities

TL;DR

This paper develops a stabilization feedback law with integral action for conservative abstract linear systems with actuator nonlinearities, ensuring stability and demonstrating effectiveness through theoretical proofs and a wave equation example.

Contribution

It introduces a novel control law that guarantees stability for systems with input nonlinearities, validated by theoretical analysis and simulation.

Findings

Proves well-posedness and global asymptotic stability of the closed-loop system.

Applies the control law to a wave equation coupled with an ODE at the boundary.

Demonstrates effectiveness through simulation results.

Abstract

In this article, we present a stabilization feedback law with integral action for conservative abstract linear systems subjected to actuator nonlinearity. Based on the designed control law, we first prove the well-posedness and global asymptotic stability of the origin of the closed-loop system by constructing a weak Lyapunov functional. Secondly, as an illustration, we apply the results to a wave equation coupled with an ordinary differential equation (ODE) at the boundary. Finally, we give the simulation results to illustrate the effectiveness of our method.