The multivariable compensator synthesis problem is a difficult one if order minimization is required. Based on duality of state feedback and state observer, time domain is an appropriate approach to design these systems. The order of a time domain controller is generally equal to the order of plant; hence the controller order reduction is an important subject in this domain. Using a reduced order state observer, the order of controller can be reduced by the number of outputs. Considering this situation and the duality concept in time domain, the possibility of controller order reduction based on the number of inputs is discussed. In fact, based on the dual relation between state feedback and state observer, the order of state feedback can be reduced. The objective of this thesis is to consider this subject which finally leads to the definition of reduced order state feedback. Presenting some relevant results, the importance of the definition of reduced order state feedback is considered in two aspects. On one hand, based on this definition, the design goals in multi input systems can be achieved with a reduced number of state variables and consequently the total control cost decreases. On the other hand, the order of observer and hence the order of time domain controller can be reduced based on the estimation of a reduced number of state variables. The techniques for the order reduction of a pole placement controller had been widely studied over the decades. So this controller is selected for design issues in this
