Interpolatory projection technique for Riccati-based feedback stabilization of index-1 descriptor systems
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The aim of the work is to stabilize the unstable index-1 descriptor systems by Riccati-based feedback stabilization via a modified form interpolatory projection-based technique Iterative Rational Krylov Algorithm (IRKA). The basic IRKA is used to find Reduced Order Models (ROMs) for the stable systems conveniently but it is unsuitable for the unstable systems. In the proposed technique, we implement the initial feedback within the construction of the projectors of the IRKA approach. The Riccati solution is estimated from the ROM achieved by IRKA and hence the low-rank feedback matrix is attained. The feedback matrix for the full model is retrieved from the low-rank feedback matrix by the reverse projecting process. Finally, the applicability and efficiency of the proposed method are validated by applying to unstable index-1 descriptor systems. The simulation is done numerically using MATLAB and the achieved results are discussed in both tabular and graphical approaches.
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