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

Mahtab Uddin,M Monir Uddin,M A Hakim Khan,Md Motlubar Rahman

doi:10.1088/1757-899x/1070/1/012022

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.

Highlights

The index-1 descriptor system of the first-order form can be written with the input-output relations by means of the sparse block-matrices asE1 0 00 x1(t) x2(t) = J1 J3 J2 J4 x1(t) x2(t) +B1 B2 u(t), E x (t) A x(t) B (1) y(t) = C1
The Riccati-based feedback stabilization technique for index-1 descriptor systems by the Rational Krylov Subspace Method (RKSM) via the Linear Quadratic Regulator (LQR) approach and the Low-Rank Cholesky-Factor integrated Alternative Direction Implicit (LRCF-ADI) based Kleinman-Newton method ware discussed [9, 10]. In both of the works, to optimally stabilize, some unstable systems are considered as the target system, those arising from the Brazilian Interconnected Power System (BIPS) models
We propose a modified form of the bi-tangential interpolation-based Iterative Rational Krylov Algorithm (IRKA) technique for the optimal feedback stabilization of those power system models

Summary

Introduction

The Riccati-based feedback stabilization technique for index-1 descriptor systems by the Rational Krylov Subspace Method (RKSM) via the Linear Quadratic Regulator (LQR) approach and the Low-Rank Cholesky-Factor integrated Alternative Direction Implicit (LRCF-ADI) based Kleinman-Newton method ware discussed [9, 10]. In both of the works, to optimally stabilize, some unstable systems are considered as the target system, those arising from the Brazilian Interconnected Power System (BIPS) models.

Numerical results

Conclusions