Optimization and Systems Theory Seminar
Friday March 25 at 11.00 Lindstedtsvägen 25, room 3721

Ruth Curtain 
Department of Mathematics and Computing Science, University of Groningen.
The Netherlands

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., A=A0n. 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.