Application specific stability of 3-D Roesser-like model realizations

Stability of multidimensional (k-D) systems is still a challenging field of work. Well known and established stability measures may lead to complex mathematical problems, while simple tests are restricted to special cases of n-D systems. A new stability test for certain discrete 3-D system realizations given in a Roesser-like model description is proposed. This test is suitable for signals bounded with respect to all three coordinate directions, like spatio temporal video image signals. The 3-D system is observed in real operation, i.e. considering a sequence of processing, which leads to a 1-D state space description, allowing for application of a 1-D stability test. Since application of 1-D stability tests to higher dimensional problems is not a completely new approach, main contribution of this paper is the regular and well structured decomposition of a discrete 3-D system description into a classical 1-D state space description.