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Existence condition of positive-definite solutions for algebraic matrix riccati equations

✍ Scribed by Hiroyuki Kano

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
453 KB
Volume
23
Category
Article
ISSN
0005-1098

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✦ Synopsis

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-loop system. The condition is stated in terms of the detectability and stabilizability of certain matrix pairs, as was the case for the non-negative-definite solution. Simple examples are included to illustrate the new results against the existing ones.

πŸ“œ SIMILAR VOLUMES

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## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^βˆ’Ξ±^__A__ = __Q__ with Ξ± ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rat