关键词: 二阶系统, Lancaster 结构, 保结构, 系统解耦, Kronecker 积

Abstract:

In numerical algebra field, the quadratic system decoupling is researched by preserving Lancaster structure, but it is difficult to find decoupling transformations, which involves the solution of nonlinear equations. A new method of numerical decoupling of quadratic system is proposed in this paper. The decoupled system is identified by the isospectrality of systems, and the nonlinear problem to solve decoupling transformations is converted to the solution of Sylvester equation. The decoupling transformations are given based on the Kronecker product knowledge of matrixes. The method is shown to be feasible by numerical experiments, and it supplies a new point for quadratic system decoupling research.

Key words: quadratic system, Lancaster structure, structure preserving, system decoupling, Kronecker product