Observability

• (*C,A*) is
observable if, for any *t**1* > 0, the initial
state *x(0) = **x**0* can be determined from the time history of
the input *u(t)* and the output *y(t)* in the interval of [*0,t**1*].

• The matrix

is positive definite for any *t *> 0.

•The
observability matrix *O *has

full column rank, i.e.,

•The
eigenvalues of *A+LC* can be freely assigned by a

suitable L.