  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.
