Modelling combined automata via semi-tensor product of matrices

Using semi-tensor product of matrices (STP), a new matrix analysis tool, this paper investigates the problem of modelling combined automata, which are constructed in three ways: parallel, serial and feedback. By representing the states, input and output symbols in vector forms, the transition and output functions are expressed as algebraic equations of the states and inputs, in which the matrix product is STP. Based on such algebraic descriptions, three new models are established for three types of combined automata with the help of STP. Illustrative examples verify the correctness of the new models.