Abstarct: In this thesis, we will introduce the detection of partial eigenvalues assingment problem. The problem of keeping one part of open-loop matrix spectrum of linear system constant, by controlling the state feedback and bring out the remaining spectrum is called ”partial eigenvalue assingment problem”. In fact this problem is used for such systems which are not completely stable and a number of open-loop spectrum eigenvalue that need re-allocation are not in stable region. Since this problem is very important in control and optimization theory numerous method have provided to solve it and some of them are investigated in this thesis. We then by using of left eigenvectors related to unstable eigenvalues, turn the problem to eigenvalue assingment problem and by making use of simillary transitions in linear control systems, we calculate the state feedback matrix which assigns desired eigenvalues to a close-loop system. Since making norm of state feedback matrix minimum is very important in optimization of linear control systems, by using of the proposed method and state transition graph, we obtain state feedback matrix which has the minimum norm. Then we introduce a new way to find non-linear parametric state feedback matrix. At the end of each section for more understanding of concepts, numerical examples are provided.