Previous papers from this laboratory have detailed a procedure for controlling dynamic linear chemical processes in an optimum manner. Involved in the method was the use of dynamic programming as developed by Bellman and extended by Kalman and consisted of minimizing a quadratic form of the state or dependent variables of the system. A brief summary of this procedure is presented in a later section of this paper. However, in certain physical situations the method is impractical because of the nature of the inputs which must be used as control variables, i.e. feed compositions must be varied instead of the more natural feed rate. In the present paper the method of Lyapunov is used to extend this dynamic control approach to allow flow rate to be used as a control variable. To illustrate the details a number of different procedures are presented ranging in complexity from a relatively simple approximation to a detailed search routine. © 1961.