Abstarct: In this thesis, we describe the partial eigenvalue assignment problem in linear control systems. This problem applied for systems that are near stability. In other words, a small number of eigenvalues of the open-loop system, aren’t in stability region and only this small number require reassigning.Given the importance of this problem in control theory and optimization, various method methods have been presented to solve it such as orthogonality relations method, Arnoldi method and ...., that we first examine these methods and then with using partial Schur decomposition method and similarity transation in linear control systems, we introduce a new method that requires less computation compared to other methods. For solving problem with this method, first, with using partial Schur decomposition we find the ortonormal basis on invariant subspace assocaited with the eigenvalues to be assigned. Then with using similarity transationt in linear control system, we compute the feedback matrix that assigned desired eigenvalues in to the closed-loop system. Given the importance of the minimization norm of the state feedback matrix in optimization of the linear control system, with using proposed method and the state transation graph , we find the state feedback matrix that is minimum norm. Finally, we solve partial eigenvalues assignment problem for stability of descrite time 2D linear control systms with proposed method. In the end of each discussion, numerical examples are given.