The Study Of Controllable Area Of Linear Continuous-time Systems' Normal Form Under The Bounded Control Function

In the 20 th century,Control theory and technology have been widely applied in many fields,and the linear control system occupies a very important position in the theory of automatic control or automatic control.In control theory,controllability,observability and stability are the basic structural characteristics of linear systems,among these controllability as one of the most classical theories,answers the question whether the state of the system can be controlled by the control function.The controllability problem is whether the control input of the system has the ability to affect each state in the system.Because of the correlation between states and the different effects of states on system characteristics,it is of great significance for linear systems to study whether the system is controllable and the controllable area.Because the control ability is always limited,the work has practical significance.So in this paper,the controllable area of linear control system is mainly studied under the condition that the control function is bounded.In the linear systems,controllability and accessibility are equivalent.And some papers have introduced the range of reachable sets for two-dimensional and threedimensional time-varying systems and stationary systems under the bounded control function.For the linear continuous-time systems,the study of the controllable region is infrequent.Because the normal form of the system has the same controllability as the corresponding system,and the normal form of the system is simpler and more unified,so i will study the controllable area of linear systems' normal form under the bounded control function in this paper.In the paper,the main tasks include: firstly,we will provide and proof the necessary and sufficient conditions for the complete controllability of a constant system under bounded control function;Secondly,for the two-dimensional constant systems under bounded control,study the relationship between controllable area and coefficient matrix;Finally,for three-dimensional linear constant systems' normal form,we will find corresponding controllable area.