There exists a controller such that only if the following conditions hold:
(i)there exists a stabilizing solution X¥ >0 to
X¥ A+A*X¥ +X¥ (B1B1*/g2-B2B2*)X¥+C1*C1=0
(ii) there exists a stabilizing solution
Y¥ >0 to
AY¥ +Y¥ A*+Y¥ (C1*C1/g2-C2*C2)Y¥+B1 B1*=0
(iii)