Research On Fault Tolerance And D-Admissibility Control Of Generalized Delta Operators

With the development of control theory,it is found that there is a more general form of the dynamic system,which is named the singular system.Compared with the normal system,the singular system is more suitable to describe the practical application system,such as electronic system,economic system,constrained mechanical system,aircraft modeling and so on.The study of singular system can promote economic development,social progress and the development of high-tech industries,and also play an important role in the development of control theory.It has been several decades since the concept of generalized system was put forward.The development of the singular system is very rapid,and now it has achieved rich theoretical results.The Delta operator method is a bridge between continuous system and discrete system,and the discrete system using Delta operator is closer to the original continuous system.It can solve the problem of the traditional shift operator in the high frequency domain,and the Delta operator method can solve the deviation of the discrete system and the continuous system in the high-speed sampling,so as to ensure the stability of the system.Fault-tolerant control is designed to improve the reliability of the system,and the fault tolerant controller can make the system run stably when some components fail.The D-admissible controller can be used to configure the closed-loop poles of the system in a circular region to improve the steady state and dynamic characteristics of the system.In this paper,the system model is a singular Delta operator system,and the faulttolerance control and D-admissible control problem are studied.The necessary and sufficient conditions for the existence of the controller are derived based on the necessary and sufficient conditions of the singular Delta operator system and the corresponding definitions,and the design method of the controller is derived by using the LMI method.Finally,an example is given to verify the correctness of the research method.The results show that the controller designed in this paper is effective and feasible.The research of this paper is of great significance to the study of practical system.