Recently, the theory of semi-tensor product (STP) method of matrices has received much attention from variety communities covering engineering, economics and industries, etc. This paper describes a detailed survey on some recent applications of the STP method in finite systems. First, some useful mathematical tools on the STP method are provided. Second, many recent developments about robustness analysis on the given finite systems are delineated, such as robust stable analysis of switched logical networks with time-delayed, robust set stabilization of Boolean control networks, event-triggered controller design for robust set stabilization of logical networks, stability analysis in distribution of probabilistic Boolean networks, and how to solve a disturbance decoupling problem by event triggered control for logical control networks. Finally, several research problems in future works are predicted.
Keywords: algebraic formulation; finite system; logical networks; robustness; semi-tensor product method of matrices.