Solvability of the H ∞ algebraic Riccati Equation in Banach algebras

Let R be a commutative complex unital semisimple Banach algebra with the involution {Mathematical expression} . Sufficient conditions are given for the existence of a stabilizing solution to the H∞ Riccati equation when the matricial data has entries from R. Applications to spatially distributed systems are discussed. © 2011 Springer Basel AG.