lyap - Lyapunov equation

Calling Sequence

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

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

Parameters

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

Description

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').
   

Examples

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
 

See Also

sylv  ctr_gram  obs_gram