Ensemble Feedback Stabilization of Linear Systems

TL;DR

This paper introduces a Riccati-based ensemble feedback method for stabilizing linear systems with parameter-dependent matrices, ensuring stability across a training set and nearby systems, with quantifiable suboptimality.

Contribution

It proposes a novel ensemble feedback stabilization approach using Riccati equations for parameter-dependent linear systems, with analysis of stability and suboptimality.

Findings

Single feedback stabilizes all training set systems

Feedback also stabilizes systems near the training set

Suboptimality of feedback can be quantified

Abstract

Stabilization of linear control systems with parameter-dependent system matrices is investigated. A Riccati based feedback mechanism is proposed and analyzed. It is constructed by means of an ensemble of parameters from a training set. This single feedback stabilizes all systems of the training set and also systems in its vicinity. Moreover its suboptimality with respect to optimal feedback for each single parameter from the training set can be quantified.