2
Lyapunov Equations
q
Consider the following Lyapunov equation
q
A*X+XA+Q =
0
q
Assume that
A
is stable, then the following statements hold:
•
X
=
•
X
> 0 if
Q
>0 and
X
³
0 if
Q
³
0
.
•
if
Q
³
0, then (
Q,A
) is observable iff
X
> 0.
q
Proof:
•