Riccati-based feedback stabilization for unstable Power system models Mahtab Uddin * , M. Monir Uddin † , and Md. Abdul Hakim Khan ‡ November 25, 2021 Abstract In this article, the objective is mainly focused on finding optimal con- trol for the large-scale sparse unstable power system models using optimal feedback matrix achieved by the Riccati-based feedback stabilization pro- cess. Our aim is to solve the Continuous-time Algebraic Riccati Equations (CAREs) governed from large-scale unstable power system models, which are of index-1 descriptor systems with a sparse pattern. We propose the projection-based Rational Krylov Subspace Method (RKSM) for the com- putation of the solution of the CAREs, the novelties of RKSM are sparsity- preserving techniques and the implementation of time convenient recursive adaptive shift parameters. We modify the machine-independent Alternat- ing Direction Implicit (ADI) technique based nested iterative Kleinman- Newton (KN) method and adjust this to solve the CAREs governed from large-scale sparse unstable power system models. We compare the results achieved by the Kleinman-Newton method with that of using the RKSM. The applicability and adaptability of the proposed methods are justified through the Brazilian Inter-Connected Power System (BIPS) models and their transient behaviors are comparatively analyzed by both tabular and graphical approaches. keywords: Riccati equation, optimal control, feedback stabilization, RKSM, Kleinman-Newton method, LRCF-ADI method, power system model 1 Introduction The dynamic of a large-scale power system model can be described by Differen- tial Algebraic Equations (DAE) as ˙ x(t)= f (x 1 ,x 2 ,P ), f : R n1+n2+n3 → R n1 , 0= g(x 1 ,x 2 ,P ), g : R n1+n2+n3 → R n2 , (1) ∗ Institute of Natural Sciences, United International University, Dhaka-1212, Bangladesh, mahtab@ins.uiu.ac.bd † Department of Mathematics and Physics, North south University, Dhaka-1229, Bangladesh, monir.uddin@northsouth.edu ‡ Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh, mahkhan@math.buet.ac.bd 1 arXiv:2006.14210v1 [math.OC] 25 Jun 2020