The discrete-time strictly bounded-real lemma and the computation of positive definite solutions to the 2-D Lyapunov equation

Four algorithms for computing positive definite solutions to the 2-D Lyapunov equation are developed. These algorithms are based on two alternative forms of the discrete-time strictly bounded-real lemma (DTSBRL) presented by the authors. Two of the algorithms use 1-D spectral factorization, the other two require the solution of a matrix Riccati equation. In all cases, the problem of solving the 2-D Lyapunov equation is reduced to solving a series of 1-D problems. Examples illustrate all methods.>