v(By completing square with respect to F to get)
Û
q $ X =X*³0 such that
q XA+A*X+XB1B1*X /g2-X B2B2*X+C1*C1
•+(F+B2*X )*(F+B2*X)=0
• and A+B2F+B1B1*X /g2 is stable.
v(Intuition suggests that F=-B2*X ) Û
q $ X =X*³0 such that
• XA+A*X+XB1B1*X /g2-X B2B2*X+C1*C1=0
• and A-B2 B2*X +B1B1*X /g2 is stable.
vÞ F=F¥ and X =X¥.
qOutput Feedback: Converting to State
Estimation
• Suppose $ a K such that ||Tzw||¥ < g
• Then x(¥ )=0 by stability (note also
x(0) = 0)