Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems

TL;DR

This paper introduces a modified IRKA-based interpolatory projection method to stabilize unstable index-1 descriptor systems via Riccati feedback, enabling effective low-rank feedback computation and validation through numerical simulations.

Contribution

A novel IRKA modification that incorporates feedback into the projection process for stabilizing unstable descriptor systems using Riccati equations.

Findings

Successfully stabilizes unstable index-1 descriptor systems.

Provides a low-rank feedback matrix estimated from reduced models.

Demonstrates effectiveness through MATLAB simulations and comparative analysis.

Abstract

The work aims to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form of Iterative Rational Krylov Algorithm (IRKA), which is a bi-tangential interpolation-based technique. In the basic IRKA, for the stable systems the Reduced Order Models (ROMs) can be found conveniently, but it is unsuitable for the unstable ones. In the proposed technique, the initial feedback is implemented within the construction of the projectors of the IRKA approach. The solution of the Riccati equation is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. Using the reverse projecting process, for the full model the optimal feedback matrix is retrieved from the low-rank feedback matrix. Finally, to validate the aptness and competency of the proposed technique it is applied to unstable index-1 descriptor systems. The comparison of the present work with two previous works is narrated. The simulation is done by numerical computation using MATLAB, and both the tabular method and graphical method are used as the supporting tools of comparative analysis.