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Methods for verified stabilizing solutio...
Haqiri, Tayyebe...

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Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations by Haqiri, Tayyebe ( Author )
Lemonjar Open Access
N.A
07-09-2015
We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuous-time algebraic Riccati equation $A^*X+XA+Q=XGX$ building on the work of [B.~Hashemi, \emph{SCAN} 2012] and adding several modifications to the Krawczyk procedure. We show that after these improvements the Krawczyk method reaches results comparable with the current state-of-the-art algorithm [Miyajima, \emph{Jpn. J. Ind. Appl. Math} 2015], and surpasses it in some examples. Moreover, we introduce a new direct method for verification which has a cubic complexity in term of the dimension of $X$, employing a fixed-point formulation of the equation inspired by the ADI procedure. The resulting methods are tested on a number of standard benchmark examples.
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https://arxiv.org/abs/1509.02015
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