Model Reduction And Controller Reduction In Linear System

Model reduction is an important tool to simplify large scale systems which got more attentions form the people. They put forward lots of effective methods about it. However, most of them focus on the continuous systems and the reduction methods about the discrete system are very few.Controllers followed by the L₁ theory are usually difficult to realize and maintain, because their orders are too high. It is an obstacle to the application of the L₁ theory.For those two reasons, this dissertation summarized the development of system reduction and advanced a new balanced truncation method for model reduction, applied in the linear discrete-time system. This method conquered disadvantages of Moore's method which can't solve the unstable system and got the error bound. Then it also proposed a new method to solve SISO L₁ controllers reduction.The main innovations are outlined as follows:1. To reduce the model of discrete time LTI systems, a new method is proposed without the limitation of stability. By using bilinear transformation between discrete time systems and continuous time systems, a continuous time model reduction method is extended to discrete time systems. An upper bound of the model reduction error is given2. Transformed the requirements of internal stability into the restriction conditions to the closed-loop system and Transformed the L₁ controller reduction to the L₁ optimization problem. Used the successive linear programming and particle swarm optimization respectively. Then gained the low-order controllerThe last part is the summary and perspective of this dissertation.