Application specific stability of 2-D Roesser 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 2-D system realizations given in a Roesser model description is proposed. This test is suitable for signals bounded with respect to both coordinate directions, like images. The 2-D system is observed in real operation, i.e. considering a sequence of processing, which leads to a 1-D state space description. The resulting 1-D system matrix is some kind of a block Toeplitz matrix that allows definition of the test.