It is often very difficult to obtain directly a desired special solution to a given problem. However, if all the solutions, in other words, the general solution, to the problem could be established, the desired particular solution can then be derived by optimizing the degrees of freedom existing in the general solution.Similarly, in order to solve a desired controller of a certain type for a given control system, we can first establish a general parametric expression for this type of controllers, and then derive the desired controller by comprehensively optimizing the design parameters in the established general parametric expression.The process of establishing the general parametric expression for a type of controllers is called controller parameterization. While the process of converting the control system design requirements into certain constraints on the parameters in the general parametric controller is called design objective parameterization. Based on these two steps, the problem of controller design for a given system can be finally converted into a static optimization problem on selecting the design parameters.In this course, several controller parameterization problems are introduced, and their solutions based on generalized eigenstructure assignment are provided. Meantime, several typical design objective parameterization problems are also discussed and solved.