Ruth Curtain

Department of Mathematics and Computing Science, University of Groningen.

The Netherlands

Over the years there has been considerable interest in the algebraic properties
of the following Riccati equation

A* X+XA-XBB*+C* C=0,

where A,B,C lies in*A*, a Banach algebra with identity,
and the involution operation *.
Conditions are sought to ensure that the Riccati equation has a
*stabilizing solution* in *A*: i.e., X in *A* satisfies
the Riccati equation and A-BB* X is stable with respect to *A*.
In this talk this question is examined for the case that A,B,C are matrices
with components in a commutative scalar Banach algebra *A*_{0}, i.e.,
* A=A*_{0}^{n}.
It turns out that X will be in this algebra only if the
involution operation satisfies certain conditions.
Applications to spatially invariant systems are discussed.

A* X+XA-XBB*+C* C=0,

where A,B,C lies in

Calendar of seminars