Stability for 2-D linear discrete systems with stochastic parameters

The present paper is concerned with stability of two-dimensional (2-D) discrete systems with stochastic parameters. First, 2-D discrete system model with stochastic parameters is established by extending system matrices of the well-known Fornasini-Marchesini's second model into stochastic matrices. The elements of these stochastic matrices are second-order, weakly stationary white noise sequences. Second, mean-square asymptotic stability is derived using linear matrix inequality theory. Our results can be seen as extensions of the 2-D linear deterministic case. Finally, an illustrative example is provided.