Late lumping of observer-based state feedback for boundary control systems

TL;DR

This paper develops an observer approximation scheme for infinite-dimensional boundary control systems, enabling finite-dimensional observer-based feedback by decomposing gains and ensuring stability through spectrum analysis.

Contribution

It introduces a novel late-lumping approach that combines bounded and unbounded gain parts for improved boundary control system design.

Findings

The scheme allows direct integration with existing controllers.

Spectral conditions ensure closed-loop stability.

The method facilitates finite-dimensional observer implementation.

Abstract

Infinite-dimensional linear systems with unbounded input and output operators are considered. For the purpose of finite-dimensional observer-based state feedback, an observer approximation scheme will be developed which can be directly combined with existing late-lumping controllers and observer output injection gains. It relies on a decomposition of the feedback gain, resp. observer output injection gain, into a bounded and an unbounded part. Based on a perturbation result, the spectrum-determined growth condition is established, for the closed loop.