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

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Document pages: 12 pages

Abstract: The work aims to stabilize the unstable index-1 descriptor systems byRiccati-based feedback stabilization via a modified form of Iterative RationalKrylov Algorithm (IRKA), which is a bi-tangential interpolation-basedtechnique. 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 theconstruction of the projectors of the IRKA approach. The solution of theRiccati equation is estimated from the ROM achieved by IRKA and hence thelow-rank feedback matrix is attained. Using the reverse projecting process, forthe full model the optimal feedback matrix is retrieved from the low-rankfeedback matrix. Finally, to validate the aptness and competency of theproposed technique it is applied to unstable index-1 descriptor systems. Thecomparison of the present work with two previous works is narrated. Thesimulation is done by numerical computation using MATLAB, and both the tabularmethod and graphical method are used as the supporting tools of comparativeanalysis.

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