User`s guide

dlyap
11-61
11dlyap
Purpose Solve discrete-time Lyapunov equations
Syntax X = dlyap(A,Q)
Description dlyap solves the discrete-time Lyapunov equation
where and are -by- matrices.
The solution is symmetric when is symmetric, and positive definite when
is positive definite and has all its eigenvalues inside the unit disk.
Diagnostics The discrete-time Lyapunov equation has a(unique)solutionif the eigenvalues
of satisfy for all .
If this condition is violated,
dlyap produces t he error message
Solution does not exist or is not unique.
See Also covar Covariance of system response to white noise
lyap Solve continuous Lyapunov equations
A
T
XA X– Q+ 0=
A
Q
n
n
X
Q
Q
A
α
1
α
2
...
α
n
,,,
A
α
i
α
j
1
≠
ij
,()