Research On Some Problems Of Generalized System Control Method

With the development of social modernization and information technology,the generalized system comes into being when the conventional linear system can no longer meet the needs of science and technology and industrial production.In comparison with the general system,the generalized system is more general and can solve the engineering problems caused by incomplete information.However,after the model is established,the stability of the system can not be guaranteed sometimes,so it is very important to adjust the stability of the system by adding controllers.In this paper,the structure and characteristics of the generalized system with control input are analyzed,including the following aspects.Firstly,we studied how to simplify the coefficient matrix of the three-dimensional generalized system after adding the control input,which is a preparation for analysis and discussion of subsequent system stability.This step was carried out under the condition that the ranks of the control matris were 3,2,1,respectively.Secondly,we analyze all the unsteady three-dimensional generalized systems with normalized coefficient matrices,and summarize the classification,we obtain the classification method of general generalized control system and the method of finding correlation transformation matrix when transforming standard form,and the three-dimensional generalized control systems can be divided into three types: First,the system stability can be changed by adding controllers.Secondly,adding controllers can only partially change the stability of some state components.Third,you can’t make the system stable by adding controllers.We also give a method to judge the types of the three-dimensional generalized control systems.An example is given to illustrate the case that an unstable three-dimensional uncertain system can become robust by adding controllers.At the same time,an example is given to illustrate that for the generalized switching control system where all subsystems are unstable,the whole system can be stabilized by designing switching rules.Finally,we summarize the specific research content and innovation,and expound the follow-up work of the paper.