Sylvester方程非奇异解的构造  

Constitution for nonsingular solution of Sylvester equation

作　　者：王淑娟[1] 张善美 沈继红[1] 

机构地区：[1]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《哈尔滨商业大学学报（自然科学版）》2011年第2期196-202,共7页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：中央高校基金"基于Lancaster结构的二阶系统解耦算法研究及其在舰船振动系统解耦中的应用"(GK2110260107)

摘　　要：对于基于Lancaster结构二阶系统的解耦问题,可以将求解解耦变换的非线性问题转化为求次Sylvester方程的非奇异解.然而,利用线性方程组的方法虽然可以求解这个问题,但是这样会产生误差以至于不能获得完全等价的解耦系统.利用齐Sylvester方程解的一种构造方法求解其非奇异解,即基于系统解耦前后具有相同谱信息进行通解形式的构造,并通过选取适当参数的方法得到一个非奇异解.为求解齐次Sylvester方程的非奇异解问题找到了一种简便可行的方法,数值试验证明了该方法的可行性.For decoupling of second order system,the nonlinear problem of decoupling transformations of system could be translated into solution about nonsingular solution of the Sylvester equation.However,as a solution method to this equation by using linear equation groups,it easily gave birth to experiment error and didn＇t even to obtain completely equivalent decoupling system.In this paper,the nonsingular solution of the Sylvester equation was solved,according to a constitution method of that equation solution,i.e.The formation of general solution was constructed by using the same spectrum information,which was achieved between pre-and post-system decoupling;second,the nonsingular solution was searched by selection of parameters.The results of numerical experiments shown this constitution method was a feasible one,which supplied a simple approach for nonsingular solution of the Sylvester equation.

关 键 词：二阶系统 SYLVESTER方程 非奇异解 系统解耦 

分 类 号：O29[理学—应用数学]