State estimation for two-dimensional linear systems with stochastic parameters

The present paper is concerned with state estimation of two-dimensional (2D) discrete stochastic systems. First, 2D discrete stochastic system model 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 which is a prerequisite for the design of state estimator is derived. Third, linear unbiased full-order state estimation problem for 2D discrete linear stochastic model is formulated. Two estimation problems considered are the designs for mean-square bounded estimation error and for the mean-square stochastic version of the suboptimal H_¿ estimator, respectively. Our results can be seen as extensions of the 2D linear deterministic case. Finally, an illustrative example is provided.