Research on Stabilization of Finite State Machine Under Function Perturbation Based on STP

This paper investigates the stabilization of finite state machines (FSMs) under function perturbations. First, by using the semi-tensor product (STP) of matrices, we derive an algebraic expression for the FSM under function perturbations. Next, based on this algebraic form, a necessary and sufficient criterion is derived, which can be used to judge whether a perturbed FSM is stabilizable to an equilibrium state. Furthermore, an algorithm for stabilizing perturbed FSMs is developed. Finally, an illustrative exmaple is provided to show the effectiveness of our method.