User`s guide

covar
11-40
11covar
Purpose Output and state covariance of a system driven by white noise
Syntax [P,Q] = covar(sys,W)
Description covar calculates the stationary covariance of the output of an LTI model sys
driven by Gaussian white noise inputs . This function handles both
continuous- and discrete-time cases.
P = covar(sys,W) returns t he steady-state output response covariance
given the noise intensity
[P,Q] = covar(sys,W) also returns the steady-state state covariance
when
sys is a state-space model (otherwise Q is set to []).
When applied to an
N-dimensional LTI array sys, covar returns
multi-dimensional a rrays P, Q such that
P(:,:,i1,...iN) and Q(:,:,i1,...iN) are t he covaria nce matrices for the
model s
ys(:,:,i1,...iN).
Example Compute the output response covariance of the discrete SISO system
due to Gaussian white noise of intensity
W = 5.Type
sys = tf([2 1],[1 0.2 0.5],0.1);
p = covar(sys,5)
y
w
PEyy
T
()=
Ewt()wτ()
T
()Wδtτ–()= (continuous time)
Ewk[]wl[]
T
()Wδ
kl
= (discrete time)
QExx
T
()=
Hz()
2z 1
+
z
2
0.2 z 0.5++
--------------------------------------
,= T
s
0.1=