Transformations between discrete-time and continuous-time algebraic Riccati equations

Transformations Between Discrete-time and Continuous-time Algebraic Riccati Equations

We introduce a transformation between the discrete-time and continuoustime algebraic Riccati equations. We show that under mild conditions the two algebraic Riccati equations can be transformed from one to another, and both algebraic Riccati equations share common Hermitian solutions. The transformation also sets up the relations about the properties, commonly in system and control setting, tha...

Discrete Time H∞ Algebraic Riccati Equations

Analytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations

This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...

Solving Large-Scale Discrete-Time Algebraic Riccati Equations by Doubling

We consider the solution of large-scale discrete-time algebraic Riccati equations with numerically low-ranked solutions. The structure-preserving doubling algorithm will be adapted, with the iterates for A not explicitly computed but in the recursive form Ak = A 2 k−1 − D (1) k S −1 k [D (2) k ] >, where D (1) k and D (2) k are low-ranked with S −1 k being small in dimension. With n being the d...

Methods for Verified Solutions to Continuous-time Algebraic Riccati Equations

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 e...