Mean Square Stability and Stabilization for Linear Parabolic Stochastic Partial Difference Systems

This paper studies the mean square stability and stabilization of linear parabolic stochastic partial difference systems, which contain space–time characteristics and stochastic noise. A definition of the mean square stability for this system is proposed. Using stochastic analysis and some mathematical analysis methods, a strict decreasing sequence is constructed to represent the expectation of the sum of squares of the state variable along the spatial dimension. The sufficient conditions of the mean square stability are established based on system parameters, and then the convergence along the time axis is rigorously proven by the Squeeze criterion. Moreover, some stabilization criteria are derived by designing a linear feedback controller. Finally, two examples are given to illustrate the effectiveness of the results.