The Researches of Quadratic System Decoupling by Optimization Method

The decoupling of quadratic systems, arising in many important application fields, has been introduced and investigated. Recently, an existence theory has been established, showing that almost all n-degree-of-freedom second-order systems can be reduced to totally independent single-degree-of-freedom subsystems by real-valued transformations. But, these transformations depending on the matrices in a rather complicated way and, hence, are difficult to construct directly and the numerical method for such decoupling has not be completed. In this paper, we transform the algebraic thought to optimization to find the decoupling transformations, and reduce the parameter number to simplify the optimization process. The numerical experiment is shown to depict our thought, and the decoupling is implemented and the calculation is easy.