Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and H ∞ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati equations. Our contribution is twofold. First, we present sufficient conditions for the existence of a unique positive definite solution. Second, we propose an accelerated algorithm to obtain the positive definite solution with the rate of convergence of any desired order. Numerical experiments strongly support that our approach performs extremely well even in the almost critical case. As a byproduct, we show that this method is capable of computing the unique negative definite solution, once it exists.
Journal of Computational and Applied Mathematics – Elsevier
Published: Aug 15, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.
All for just $49/month
Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.
Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.
It’s easy to organize your research with our built-in tools.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera