Finite state test for asymptotic stability of two-dimensional shift-variant discrete systems

Test theorems and their algorithms for asymptotic stability test of two-dimensional (2-D) shift-variant discrete systems are presented and proved. Compared with the classical results about stability of 1-D shift-variant discrete systems, our criteria are based on finite states of system matrices of the shift-variant discrete systems, and they are necessary and sufficient conditions for asymptotic stability of 1-D and 2-D shift-variant discrete systems. The criteria are of simpler forms for their on-line applications. Examples are given to illustrate the difference of stability criteria between shift-variant discrete systems and shift-invariant discrete systems.