lyap

Arguments

A, C

real square matrices, C must be symmetric

Description

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').

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 — Solve the Sylvester equations A*X + X*B = C or A*X*B + X = C
• ctr_gram — controllability gramian
• obs_gram — observability gramian