The Research On Keeping The Same Spectral Properties Of Quadratic System Decoupling Based On Lancaster Stucture

The quadratic system is a form of control systems according to the classification of mathematical model, which is described by quadratic differential equation. Quadratic system decoupling,is a method which converts an n-dimensional multi-degree quadratic system into n unrelated one-dimensional single degree subsystems through the appropriate method. In case of unknown system spectrum information, it has important significance to study the numerical implementation of quadratic system and it is in great need in the engineering application. Currently, structure preserving isopectral flows algorithm is the unique method whose spectrum information is unknown to achieve quadratic system decoupling, which establishes spectrum flow system and controls its convergence by keeping the Lancaster structure. But there are some shortages in the design of the algorithm, which leads to some problems in the application of algorithm. And the numerical iteration of the algorithm can not be tracked, which makes the algorithm can not be controlled and corrected. On the basis of existing theories,it is very important to establish a new numerical solution.In this paper, we had a further study of structure preserving isopectral flows algorithm in the numerical decoupling algorithm which was based on the quadratic system. Firstly, we analyzed the cause of the failure examples by taking advantage of these failure examples of SPIF algorithm. And we corrected the matrix inverse operation in the algorithm and the estimation of free parameters matrix by the Tikhonov regularization method. Then, using the MATLAB, we verified the effectiveness of the modified algorithm by numerical experiments.Secondly, according to the system characteristics of the same spectrum before and after decoupling,we proposed a structure preserving isopectral flows algorithm upon the similarity transform which was based on the analysis and deduction in the special conditions of existing algorithms. Upon the basis of the algorithm, we concentrated on the failure examples of SPIF algorithm to process some numerical simulation experiments by MATLAB. The results showed that the validity of the proposed algorithm was verified meanwhile.We studied the shortages of the SPIF algorithm in the article, and not only did we make an effective correction to the algorithm, but also put forward to a more effective numerical algorithm. It put emphasis up on the study of the quadratic system decoupling numerical implementation which was under the condition that the spectrum information was unknown,and it had practical significance.