Square-root solver for discrete-time Lyapunov equations

`R = dlyapchol(A,B)`

X = dlyapchol(A,B,E)

`R = dlyapchol(A,B)`

computes a Cholesky
factorization `X = R'*R`

of the solution `X`

to
the Lyapunov matrix equation:

A*X*A'- X + B*B' = 0

All eigenvalues of `A`

matrix must lie in the
open unit disk for `R`

to exist.

`X = dlyapchol(A,B,E)`

computes a Cholesky
factorization `X = R'*R`

of `X`

solving
the Sylvester equation

A*X*A' - E*X*E' + B*B' = 0

All generalized eigenvalues of (`A`

,`E`

)
must lie in the open unit disk for `R`

to exist.

[1] Bartels, R.H. and G.W. Stewart, "Solution
of the Matrix Equation AX + XB = C," *Comm. of the ACM*,
Vol. 15, No. 9, 1972.

[2] Hammarling, S.J., "Numerical solution
of the stable, non-negative definite Lyapunov equation," *IMA
J. Num. Anal.*, Vol. 2, pp. 303-325, 1982.

[3] Penzl, T., "Numerical solution
of generalized Lyapunov equations," *Advances in
Comp. Math.*, Vol. 8, pp. 33-48, 1998.

Was this topic helpful?