•An ARE may
have many solutions. We are only interested in symmetric solutions. In particular,
we are interested in the symmetric solution such that A+RX is stable. This solution
is called stabilizing
•Consider the associated
•so H and -H* are similar.Thus l is an eigenvalue iff - l* is.
qThus we conclude: eig(H) ¹ jwÛH has n eigenvalues in Re s<0 and n eigenvalues in Re s>0.