Specifications

covar
16-42
16covar
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 the 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 arrays P, Q such that
P(:,:,i1,...iN) and Q(:,:,i1,...iN) are the covariance matrices for the
model s
ys(:,:,i1,...iN).
Example Compute the output response covariance of the discrete SISO system
duetoGaussianwhitenoiseofintensity
W = 5.Type
sys = tf([2 1],[1 0.2 0.5],0.1);
p = covar(sys,5)
and MATLAB returns
y
w
PEyy
T
()
=
Ewt
()
w
τ()
T
()
W
δ
t
τ
–
()
= (continuous time)
Ewk
[]
wl
[]
T
()
W
δ
kl
= (discrete time)
QExx
T
()
=
Hz
()
2z 1+
z
2
0.2z 0.5++
--------------------------------------
,= T
s
0.1=