In minisymposium: Matrix Equations
Mon 17:30–18:00, Room AV 02.17We present a method which uses interval arithmetic to compute a certified solution enclosure for the stabilizing solution $X_s$ of a dense continuous-time algebraic Riccati equation $A^*X+XA+Q=XGX$. The algorithm is based on the modified Krawczyk's method used e.g. in [1], and includes a few improvements such as a preprocessing of the equation using permuted bases methods [2]. The algorithm has been tested on a suite of standard benchmark examples, and achieves results comparable to the state-of-the-art method in [3], surpassing it in some examples. An alternative algorithm which does not require the approximate diagonalization of the closed-loop matrix $A-GX_s$, based on a different fixed-point formulation, is also presented.
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- Shinya Miyajima. Fast verified computation for solutions of continuous-time algebraic Riccati equations. Jpn. J. Ind. Appl. Math., 32(2):529–544, 2015.