Analysis of the Lyapunov Function Characteristics for the Minimal-Time Circuit Design Strategy Prediction

General methodology for the system design was elaborated by means of the optimal control theory approach. The problem of the system design can be formulated in this case as a classical problem of the optimal control for some functional minimization. In this context the aim of the optimal control is to result to zero of all right hand sides of the main system of the differential equations for the final time and to minimize the total computer time. The minimal time system design algorithm was defined as the problem of functional minimization. By this methodology the aim of the system design process with minimal computer time is presented as a transition process of some dynamic system that has the minimal transition time. The optimal sequence of the control vector switch points was determined as a principal characteristic of the minimal-time system design algorithm. The different forms of the Lyapunov function were proposed to analyze the behavior of a design process. The special function that is a combination of Lyapunov function and its time derivative was proposed to predict the optimal control vector structure to construct a minimal-time system design algorithm.