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

Authors

1 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

3 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran. Member of Young Researchers Society of Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

This paper focuses on studying the interval continuous-time algebraic Riccati equation AX + 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 solution set based on a modified variant of the Krawczyk method which enables us to reduce the computational complexity, significantly. Various numerical experiments are also given to show the efficiency of proposed scheme.

Keywords


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