lyap¶

Lyapunov equation

Calling Sequence¶

[X]=lyap(A,C,'c')
[X]=lyap(A,C,'d')

:A, C real square matrices, C must be symmetric :

X= lyap(A,C,flag) solves the continuous time or discrete time matrix Lyapunov matrix equation:

A'*X + X*A = C       ( flag='c' )
A'*X*A - X = C       ( flag='d' )

Note that a unique solution exist if and only if an eigenvalue of A is not an eigenvalue of -A ( flag=’c’) or 1 over an eigenvalue of A ( flag=’d’).

A=`rand`_(4,4);C=`rand`_(A);C=C+C';
X=lyap(A,C,'c');
A'*X + X*A -C
X=lyap(A,C,'d');
A'*X*A - X -C