The Research On Decoupling Condition Of The Quadratic System And Sovling Of The Decoupling Transformation

Quadratic systems frequently appear in vibration system, fruid dynamics, signal system,the impact of noise, vibration circuit and other applications. For characterization of quadraticsystem, decoupling of quadratic system is essential. The field of numerical algebraic makelinearization of the system through Lancaster structure matrix, in order to find the coordinatetransformation to make three parameters of Lancaster structure matrix simultaneouslydiagonalization, we achieve the decoupling of quadratic system.For the problem about whether the quadratic system can be decoupled, the article firststudy decoupling conditon about the different quadratic of nonlinear system and system oflinear; Through the jordan standard form of the quadratic system, giving sufficient andnecessary conditon of general quadratic exist complex decoupling system and real decouplingsystem, and two important consise context; Finally, this parper expounds the decouplingsystem must exit the decoupling transformation of keeping structure.When the system satisfies the decoupling condition, aiming at the problem of solving thedecoupling transformation, the paper give the method of construct decoupling transformationbased on keeping structure transformation theory. The method is, through the originalcharacteristic information and parameter matrix selection, direct to construct the decouplingtransformation, and gives the theorem and the corresponding proof. The decouplingtransformation makes three parameters of Lancaster structure matrix simultaneouslydiagonalization, to get the same spectrum of decoupling system. Numerical experimentsverify the feasibility of the method.Comparising the method of sovling of decoupling transformation based on the firstSylvester matric equation, structuring decoupling transformation to decouple system is simpleand feasible, to improve the research on decoupling of the quadratic system.