Optimization and Systems Theory Seminar
Friday March 25 at 11.00 Lindstedtsvägen 25, room 3721
Department of Mathematics and Computing Science, University of Groningen.
Algebraic properties of Riccati equations
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 A0, i.e.,
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.
Calendar of seminars
Last update: January 26, 2011.