الفهرس 
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Abstract
The aim of this thesis is to consider two of the most studied problems in optimal control which are the eigenvalue assignment problem (EAP) and the static output feedback (SOF)< design problem.The attempt is to consider various formulations of the two problems stated as matrix optimization problems. The goal is to propose some ecient optimization methods to compute the local solutions of the optimization problems. In particular nonlinear hybrid conjugate gradient methods and derivative{free optimization methods are proposed to tackle these problems. The performance of the methods is demonstrated on several test problems from the literature.