2-D LYAPUNOV EQUATION AND FILTER DESIGN BASED ON THE FORNASINI-MARCHESINI 2ND MODEL

A two-dimensional (2-D) Lyapunov equation with constant coefficients i s considered for the Fornasini-Marchesini second local state-space (LS S) model. First, a novel criterion relating to the Lyapunov equation i s presented that sufficiently guarantees the asymptotic stability. A s ufficiency condition that ensures the absence of limit cycles is also given. Next, the above stability condition is incorporated into the 2- D filter structure to design 2-D state-space digital filters with guar anteed asymptotic stability. An efficient method is then developed for computing the characteristic polynomial and the inverse of the system matrix. Finally, two numerical examples are given to design 2-D stabl e state-space digital filters.