The computation of positive definite solutions to the 2-D Lyapunov equation via a matrix Riccati equation

Two algorithms for computing positive definite solutions to the 2-D Lyapunov equation are presented, based on the discrete-time strictly-bounded-real lemma. These algorithms require the solution of a matrix Riccati equation and are based on the algebraic solution of the spectral factorization problem. The problem of solving the 2-D Lyapunov equation is reduced to solving a series of 1-D problems. Examples illustrate the proposed algorithms.<>