Specifications

dlyap
16-62
16dlyap
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 Thediscrete-time Lyapunov equationhas a(unique) solution if the eigenvalues
of satisfy for all .
If this condition is violated,
dlyap produces the 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=
AQnn
XQ
QA
α
1
α
2
...
α
n
,,,
A
α
i
α
j
1
≠
ij
,()