Asymptotic stability of two-dimensional continuous Roesser models with singularities at the stability boundary

It is shown that the existence of a negative semidefinite solution Q of the Lyapunov equation A^TP+AP = Q with a positive definite block diagonal matrix P = P^T together with simple additional conditions is sufficient to guarantee asymptotic stability. The stability conditions presented can be used to study a wider range of dynamical systems, including systems with singularities at the stability boundary, which cannot be exponentially stable.