qAn A-invariant subspace S Ì Cn is called a stable invariant
subspace if all the eigenvalues of A constrained to S have negative real parts.
q Stable invariant subspaces are used to compute the
stabilizing solutions of the algebraic Riccati equations.
qExample: Let A be such that
•
•
•
• with Re l1<0, l3<0, and l4>0. Then it is easy to
verify that
• S1=span{x1}, S12=span{x1
, x2}, S123=span{x1 , x2 , x3}, S3=span{x3}, S13=span{x1 , x3}, S124=span{x1 , x2 , x4}, S4=span{x4}, S14=span{x1
, x4}, S34=span{x3 , x4}
• are all A-invariant subspaces.
Moreover, S1, S3, S12, S13, and S123 are stable A-invariant subspaces.
q