A constructive method for estimating liapunov function of large scale non-linear systems

The main theme of this thesis is oriented toward two objectives. The first one is to study the stability of large-scale system and how to decompose such systems into lower interconnected subsystems. As it is known, the main difficulty in studying stability of differential equation by the second direct method of liapunov, is the construction of Liapunov fuctions. Therefore, the second objective is oriented towards introducing a new approach for constructing Liapunov function, uses the optimization techniques in connection with the method of variable gradient method. Then improving this approach to study the stability of large-scale systems using two approaches.