qAlgebraic Riccati Equation:
q A*X+XA+XRX+Q=0,
R=R*, Q=Q*
• 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
solution.
• Consider the associated
Hamiltonian matrix:
•
• Then
•
• so H and -H* are similar. Thus l is an eigenvalue iff - l* is.
qThus we conclude: eig(H) ¹ jw Û H has n eigenvalues in Re s<0 and n eigenvalues in Re s>0.