dx/dt = Ax + Bu + v
y = Cx + Du + w

dxe/dt = Axe + Bu + L (y - Cxe - Du)
e = x - xe

de/dt = Ae + v - L (y - Cxe - Du)
de/dt = Ae + v - L (Cx + Du + w - Cxe - Du)
de/dt = (A-LC)e + eta
eta = v - L w

dx/dt = A x + B u + L (y - C x)
x(0) = E{xo}

Separação (só estimação):

S = 1/2 int(v' V^-1 v + w' W^-1 w)

dx/dt = Ax + v
y = Cx + w

H = 1/2 v' V^-1 v + 1/2 (y - Cx)' W^-1 (y - Cx) + lambda' (Ax + v)

dH/dlambda = dx/dt = A x + v
-dH/dx = dlambda/dt = C' W^-1 (y - Cx) - A lambda
dH/dv = 0 = V^-1 v + lambda

lambda = -V^-1 v
dx/dt = A x - V lambda
dlambda/dt = C' W^-1 (y - Cx) - A lambda
x = P lambda

P dlamda/dt = P C' W^-1 (y - C P lambda) - P A lambda
P dlamda/dt + dP/dt lambda = A P lambda + V lambda

y=0
dP/dt = A P + P A - P C' W^-1 C P + V