Abstarct: In this thesis, we describe the optimization singular value decomposition method and its application of the singular system .as in most engineering problems, we encounter systemes has a singular coefficient matrix, therefore, finding the best solution of this system is an effective step in advancing the practical purposes of this problem. therefore the importance of this problem, methods baxsed on singular value decomposition such as Tikhonov regularization method and truncated singular value decomposition and etc is presented to solve this problems. we first review and compare these methods and then using a new multistage method to find a solution to these problems. also, with the introduction of the inverse kinematics methods Samples optimization of singular value decomposition and its application is presented. Finally, we obtained state feedback matrix using eigenstructure decoupling . also, using this method and similarity transformations and the importance of minimizing the norm of the state feedback matrix in the optimization of linear control system, a new method is proposed to achieve this goal. At the end of each chapter, numerical examples are given to illustrate more.