Solvability of the $H^\infty$ algebraic Riccati equation in Banach algebras

Details Solvability of the $H^\infty$ algebraic Riccati equation in Banach algebras Solvability of the $H^\infty$ algebraic Riccati equation in Banach algebras

2011-07-26

arxiv.org/abs/1107.5187v1

Mathematics

Optimization and Control

7 pages, 0 figures, submitted for publication in a journal

Scientific paper

Let $R$ be a commutative complex unital semisimple Banach algebra with the
involution $\cdot ^\star$. Sufficient conditions are given for the existence of
a stabilizing solution to the $H^\infty$ Riccati equation when the matricial
data has entries from $R$. Applications to spatially distributed systems are
discussed.

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