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
Positive definite solutions of some matrix equations
✍ Scribed by Aleksandar S. Cvetković; Gradimir V. Milovanović
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 162 KB
- Volume
- 429
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.
📜 SIMILAR VOLUMES
In this paper we investigate nonlinear matrix equations X ± A \* X -q A = Q where q ≥ 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
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-
## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^−α^__A__ = __Q__ with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rat
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.