Riccati Equationbased Stabilization of Large Scale Dynamical Systems.pdfVIP

Riccati Equation-based Stabilization of Large Scale Dynamical Systems X. Rao and K. A. Gallivan P. Van Do oren Florida State University CESAME { Universite catholique de Louvain Tallahassee FL, 32306 Av. G. Lema^tre, 4, B-1348 Louvain-la-Neuve, Belgium fgallivan g@cs.fsu.edu vdooren@csam.ucl.ac.be Abstract gence diÆculties. Details on all of the algorithms can b e found in [2]. In this pap er we discuss the stabilization of large scale linear time invariant dynamical systems via feedback. In Saads pro jection algorithm, a left invariant subspace EÆcient schemes based on the Discrete Riccati Dier- V 0 of A (with presumably small dimension), that con- ence Equation are presented. tains the left unstable invariant subspace of A is com- puted. There are two ma jor classes of metho ds that can b e used. The rst computes the unstable eigenvalues and recovers their eigenvectors by some form of inverse 1 Intro duction iteration. The second class computes the basis directly by subspace iteration-like metho ds. The low-order pro- In this pap er, we fo cus on the stabilization of a discrete- jected syst