This paper develops a matrix approach to the solution of the measurement and control problems in synchronous sequential machines. The control problem in sequential machines is concerned with finding input sequences that take a given machine from a known initial state to a predesignated terminal state. There may be many different measurement problems of interest in sequential machines. One important measurement problem is the identification of the unknown initial state of the machine, called the initial-state identification problem or diagnosing problem; another important measurement problem is the identification of the terminal state of the machine, known as the terminal-state identification problem or homing problem, of which a special case is the synchronizing problem. These measurement problems may be solved by applying predetermined input sequences to the machine and noting the resulting output sequences. The conventional approach to the solution of these measurement and control problems is to make use of the information contained in the transition table of the machine in conjunction with its response tree, which is basically an exhaustive tree search process. In the present paper, instead of using the transition table and the corresponding response tree, we use only the transition matrix representation of the machine and its higher order forms to solve the aforementioned problems. The suggested approach is very systematic and completely algorithmic, and thus lends itself to easy computer implementation.