METHODS FOR VERIFIED SOLUTIONS TO CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATIONS
Tayyebe Haqiri, Federico Poloni · arXiv (Cornell University) · 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 AX + 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 3 ) 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.