In this book the implementation of the Lyapunov functional to the parametric optimization for varies systems with delays is presented. It was shown that the value of the Lyapunov functional at initial state of the system is equal to the value of the square performance index of quality in the parametric optimization problem. It was given the method to obtain the analytical formulas for the coefficients of the functional to make possible calculation of the value of the functional at initial state of the system with time delay. In this book many examples of application of the Lyapunov functional in parametric optimization to the automatic control systems are given. This book can be helpful for automatic control students.