一类关于Sylvester方程特殊形式的解

A class of solution of Sylvester equation with special structure

一个多变量系统转化为单变量二阶系统,并解除变量之间耦合关系是系统稳定性研究的重要方向.虽然一般的二阶系统方程可通过Lancaster结构转变为具有特殊结构的齐次Sylvester方程,然而对于此类方程的求解大多只能得到惟一零解或者利用非齐次方程迭代产生数值解的形式,均无法实现二阶系统有效解耦的目的.根据具有特殊结构齐次Sylvester方程非奇异解存在性问题的研究,对其结构探讨获得非奇异解的形式,并讨论一个高阶系统通过何种运算方式找到非奇异解达到解耦的目的,数值试验证明了该方法的可行性.

Multi- degree- of- freedom quadratic system can be linked with multiple totally independent single -degree- of- freedom quadratic subsystems. It has an important practi： cal significance to study on and analyze the characteristics of quadratic systems deeply. How- ever, only zero solution or number of solution can be obtained by directly applying solving method of similar equation, and effective method of nonsingular solution of the Sylvester e- quation can not be found. In this paper, the nonsingular solution of the Sylvester equation was solved, according to a constitution method of that equation solution, the formation of gen- eral solution was constructed by using the same spectrum information;the nonsingular solution was searched by estimation of parameters. The results of numerical experiments shown this constitution method was a feasible one, which supplied a simple approach for nonsingular so- lution of the Sylvester equation.