Stability and Stabilization of 2D Discrete Stochastic Fornasini-Marchesini Second Model

Abstract

This paper deals with the problem of stability and stabilization of two-dimensional (2D) discrete stochastic Fornasini-Marchesini (FM) second model. The proposed results are presented in a Linear Matrix Inequality (LMI) framework. A mean square asymptotic stablilty condition is elaborated through the use of the Leibniz-Newton formula with additional free weighting matrices. Moreover, a sufficient condition is established for the design of a state feedback controller that ensures the mean square stability of the closed loop system. In order to illustrate the effectiveness of the proposed approach, numerical examples have been given.