Abstract
In this paper we study the classical control problems by model reduction for linear second-order systems. We presentsthe ways by the typical method and the meanings about the actions of the processes . About the Lyapunov equation, we give a method called Uzawa-like iteration to accurate the solution and compare the solution with the typical method and the new method. Moreover, we find the operator to fold the mixed equation to standard equation. Finally, we give a numerical data to present the result.