qChapter 12 studies the stabilizing solution to an Algebraic Riccati Equation (ARE):
qI.e., A+RX is stable.
qSuppose H has no jw-axis eigenvalues and X-(H) is the stable invariant subspace
of H and suppose X1 is nonsingular, then X=Ric(H):=X2 X1-1 is the stabilizing solution. A key result of
this chapter is the so-called Bounded Real Lemma: G(s)ÎRH¥with ||G(s)||¥<1 if and only if there exists an X such that A+BB*X/g2 is stable and