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

This paper mainly studies the controllability of finite state machines (FSMs) whose state was perturbed during the transition. First, the FSM is transformed into its algebraic form by using the semi-tensor product (STP) of matrices method. Under the algebraic framework, a controllability matrix is constructed to determine the controllability of the perturbed FSMs. Then necessary and sufficient controllability conditions are derived. Finally, the effectiveness of our results is shown through an illustrative example.