### Optimization and Systems Theory Seminar

Friday, May 15, 1998, 11.00-12.00, Room 3733,
Lindstedtsvägen 25

**Professor Ji-Guang Sun**

Department of Computing Science

Umeå University

E-mail: jisun@cs.umu .se

####
Perturbation theory for algebraic Riccati equations

Consider the continuous-time algebraic Riccati equation (CARE)

Q+A^HX+XA-XBR^{-1}B^HX=0,

and the discrete-time algebraic Riccati equation (DARE)

X-A^HXA+(A^HXB+S)(R+B^HXB)^{-1}(B^HXA+S^H)-C^HC=0.

Appropriate assumptions on the coefficient matrices
guarantee the existence and uniqueness of the
Hermitian positive semi-definite (p.s.d.) solution (or the stabilizing
solution).
The central question of perturbation theory for an algebraic Riccati
equation is: How does the Hermitian p.s.d. solution (or the
stabilizing solution) X change when the coefficient matrices are
subject to perturbations. In this talk, we describe a technique for
obtaining new perturbation results of the CARE and the DARE. The new
results are derived in a uniform manner, and which improve the
existing results in the literature.

Calendar of seminars

*Last update: May 14, 1998 by
Anders Forsgren,
andersf@math.kth.se.
*