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.