On the square-root method for continuous-time algebraic Riccati equations
نویسندگان
چکیده
منابع مشابه
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...
متن کاملMethods 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...
متن کاملTransformations 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...
متن کاملSolving large-scale continuous-time algebraic Riccati equations by doubling
We consider the solution of large-scale algebraic Riccati equations with numerically lowranked solutions. For the discrete-time case, the structure-preserving doubling algorithm has been 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 ] >, with D (1) k and D (2) k being low-ranked and S −1 k being small in dimension. For t...
متن کاملOn a Newton-Like Method for Solving Algebraic Riccati Equations
An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newton-like method under the strong hypothesis of controllability, while the original Newton’s method needs only the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
سال: 1999
ISSN: 0334-2700,1839-4078
DOI: 10.1017/s0334270000010547