Output Feedback Stabilization For Linear Systems Based On Model Reduction

Differential equation model is an important way to construct complex linear systems.However,with the increase of the complexity of the system and the improvement of the system precision requirements,the dimension of the differential equation model becomes very large,which makes it difficult to simulate and control the system.We need to overcome these difficulties to simulate and control the actual system more effectively.Model reduction provides an effective method to solve this problem.In this paper,the output feedback controller is designed for several large-scale unstable linear systems by model reduction methods,and the corresponding design algorithms are presented.At the same time,numerical examples are given to illustrate the feasibility and effectiveness of the algorithms.In chapter 1,the background and significance of linear systems are introduced,and the model reduction methods and feedback controller design methods of several kinds of linear systems are introduced.In chapter 2,the output feedback design is investigated for large-scale unstable second-order systems.First,based on the second-order Krylov subspace method,a low dimensional second-order system is derived.Then,applying matrix transformation,the state of the low dimensional system is transformed into the output variables of the system,so that the relationship between input variables and output variables is directly established in the low dimensional system.We design output feedback controller for this system.Finally,using the argument principle,a computable stability criterion is presented to check the stability of the closed-loop system.In chapter 3,the output feedback stabilization is considered for large-scale unstable second-order singular systems.First,the upper bound of all unstable eigenvalues of secondorder singular systems is derived.Then,using the argument principle,a computable stability criterion is proposed to check the stability of second-order singular systems.Finally,applying model reduction methods to original systems,a static output feedback stabilization algorithm for second-order singular systems is presented.In chapter 4,the output feedback design is analyzed for large-scale unstable linear systems with multiple delays.First,based on two-level orthogonal Arnoldi process,a structure-preserving low-dimensional time-delay system is obtained.Then,the state of the low dimensional time-delay system is transformed into the output variables of the system through linear transformation,thus the input-output relationship of the system is established directly,and then we design the output feedback controller for this system.Finally,substituting the output feedback controller into the original system,we check the stability of the closed-loop system by using the argument principle.In chapter 5,we summarize the main contents of this paper and give the research direction in the future.