To implement the balancing based model reduction of large-scale dynamical systems we need to compute the low-rank (controllability and observability) Gramian factors by solving Lyapunov equations. In recent time, Rational Krylov Subspace Method (RKSM) is considered as one of the efficient methods for solving the Lyapunov equations of large-scale sparse dynamical systems. The method is well established for solving the Lyapunov equations of the standard or generalized state space systems. In this paper, we develop algorithms for solving the Lyapunov equations for large-sparse structured descriptor system of index-1. The resulting algorithm is applied for the balancing based model reduction of large sparse power system model. Numerical results are presented to show the efficiency and capability of the proposed algorithm.
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.
The ascendancy of coronavirus has become widespread all around the world. For the prevention of viral transmission, the pattern of disease is explored. Epidemiological modeling is a vital component of the research. These models assist in studying various aspects of infectious diseases, such as death, recovery, and infection rates. Coronavirus trends across several countries may analyze sufficiently using SIR, SEIR, and SIQR models. Across this study, we propose two modified versions of the SEIRD method for evaluating the transmission of this infectious disease in the South Asian countries, more precisely, in the south Asian subcontinent. The SEIRD model is updated further by fusing some new factors, namely, isolation for the suspected people and recovery and death of the people who are not under the coverage of healthcare schemes or reluctant to receive treatment for various catastrophes. We will investigate the influences of those ingredients on public health-related issues. Finally, we will predict and display the infection scenario and relevant elements with the concluding remarks through the statistical analysis.
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