Lyapunov function behavior analysis for different design strategies

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. 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 Lyapunov function of the design process was proposed to analyze the total design time. The special function that is a combination of Lyapunov function and its time derivative was proposed to predict the optimal control vector structure and to compare the different design strategies that compose the structural design basis.