New stability results for 2-D discrete systems based on the Fornasini-Marchesini state space model

New conditions for the internal stability of a 2-D discrete system described by the Fornasini-Marchesini (FM) local state-space model are presented. Further, the stability margin of a 2-D discrete system described by a (FM) state-space model is considered and methods to compute it or to obtain lower bounds are developed. These methods are based on the various forms of the Lyapunov equation for 2-D systems. Finally, a sufficient condition for the system to remain stable under parameter variations is presented