Input-Output Data-Driven Stabilization of Continuous-Time Linear MIMO Systems

TL;DR

This paper presents a data-driven method for stabilizing continuous-time MIMO systems using input-output data and Kreisselmeier's adaptive filter, avoiding the need for uniform observability.

Contribution

It introduces a novel approach that interprets the adaptive filter as an observer, enabling stabilization without minimal realizations or uniform observability assumptions.

Findings

Derives a linear matrix inequality for feedback gain computation.

Applicable to a broad class of continuous-time MIMO systems.

Eliminates the need for uniform observability index.

Abstract

In this paper, we address the problem of data-driven stabilization of continuous-time multi-input multi-output (MIMO) linear time-invariant systems using the input-output data collected from an experiment. Building on recent results for data-driven output-feedback control based on non-minimal realizations, we propose an approach that can be applied to a broad class of continuous-time MIMO systems without requiring a uniform observability index. The key idea is to show that Kreisselmeier's adaptive filter can be interpreted as an observer of a stabilizable non-minimal realization of the plant. Then, by postprocessing the input-output data with such a filter, we derive a linear matrix inequality that yields the feedback gain of a dynamic output-feedback stabilizer.