Methods for Verified Solutions to Continuous-time Algebraic Riccati Equations
نویسندگان
چکیده
We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuoustime algebraic Riccati equation A∗X + XA + Q = XGX, building on the work of [B. Hashemi, SCAN 2012] and adding several modifications to the Krawczyk procedure. Moreover, we describe a new O(n) direct method for verification, based on a fixed-point formulation of the equation inspired by the ADI procedure. The resulting methods are tested on a number of standard benchmark examples, and are competitive with the state-of-the-art methods for the same problem. [2010]65M32, 35Kxx, 65T60. Algebraic Riccati equation, interval arithmetic, modified Krawczyk operator, verified computation, stabilizing solution.
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