Abstract: It has been a very attractive problem to stabilize large scale system by local state feedback since 1970's. However, this problem has not been solved completely even for linear time-invariant large scale systems, For nonlinear time-invariant large scale systems, most of the researches deal with systems which interconnection gi（x）, i =1, 2, ..., N, among subsystems can be factorized as gi（x）=BiFi（x）, i = 1, 2, ..., N, are the input matrices of the subsystems. Besides, the problem of stability domain estimation was also considered. In this paper, in order to stabilize nonlinear time-invariant large scale systems by local state feedback and to determine its stability domain, linear quadratic design and a technique to define a quadratic Lyapunov function from the positive solution of N decoupled Riccati algebraic equations were employed. The presented method can be used to deal with a wider class of systems without demanding gi（x）=BiFi（x ）. As a result, procedure gives larger stability domain. So, it is possible to achieve a certain stability domain by local state feedback with small gain. For "minimal strongly connected systems" and other systems with similar property, the method is quite effective and the pro-ceduce is simple. As an application to the decentralized stabilization of a large scale telescope, the method here gives better results in comparison with others available in the literatures,