On the existence of extremal positive definite solutions of the nonlinear matrix equation
โ Scribed by A.M. Sarhan; Naglaa M. El-Shazly; Enas M. Shehata
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 659 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0895-7177
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^โฮฑ^__A__ = __Q__ with ฮฑ โ (0, โ) are given. Iterative methods to obtain the positive definite solutions are established and the rat
In this paper, the Hermitian positive definite solutions of the matrix equation X s + A \* X -t A = Q are considered, where Q is an Hermitian positive definite matrix, s and t are positive integers. Necessary and sufficient conditions for the existence of an Hermitian positive definite solution are
In this paper we investigate nonlinear matrix equations X ยฑ A \* X -q A = Q where q โฅ 1. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X + A \* X -q A = Q to have two
A conjecture that the nonlinear matrix equation always has a unique Hermitian positive definite solution is proved. Some bounds of the unique Hermitian positive definite solution are given.
Algebraic matrix Riccati equations are considered which arise in the optimal filtering as well as in control problems of continuous time-invariant systems. A necessary and sufficient condition is established for the existence of unique positivedefinite solutions and the asymptotically stable closed-