Stability and stabilization of uncertain 2-D discrete systems with stochastic perturbation

This paper is concerned with the problem of stability analysis and stabilization of two-dimensional (2-D) discrete systems with stochastic perturbation. The 2-D stochastic system model is first established based on the Fornasini-Marchesini local state-space (FMLSS) model, and mean-square asymptotic stability is derived by means of linear matrix inequality (LMI) technique. This stability result is further extended to more general cases where the system matrices also contain uncertain parameters. The most frequently used ways of dealing with parameter uncertainties, including polytopic and norm-bounded characterizations, have been taken into consideration. Based on this, the robust stabilization problem for 2-D systems with both deterministic and stochastic uncertainties is addressed, with sufficient LMI conditions obtained for the existence of stabilizing controllers, which can be solved via efficient numerical algorithms. An illustrative example is provided to demonstrate the applicability of the proposed approach.