Study On The Control And Filtering Approach For Piecewise Systems

The piecewise system is a powerful tool to study the nonlinear system.It has been widely concerned in the control theory research and engineering application.In the actual control system,the controller design is one of the most critical part,due to the controller at work by a series of effects,so we have to consider its uncertain factors.In addition,with the development of science and technology,the structure of the control system becomes more and more complex,coupled with some unavoidable interference from external factors,resulting in the system in the actuator failures and the sensor failures will be able to malfunction.Then,to ensure the normal operation of the system controllers and the system reliability and security has become the focus of attention.Therefore,the study of the robust control problem of the piecewise system is very practical.In view of the problems encountered in the above two practical projects,this paper analyzes the resilient control of the piecewise system and the problem of reliable control and filtering,and takes the example simulation method to verify the algorithm designed in this paper.This paper analyzes and studies the resilient control problem for a class of uncertain discrete-time and time delays piecewise systems.Firstly,the stability of the system is studied by using the Lyapunov stability theory and choosing the appropriate discrete piecewise Lyapunov function.On this basis,the H_? performance index and l₂-l_? performance index of the system are further analyzed and studied,and a robust resilient controller satisfying the performance index is designed so that the system controller can still work normally when the system controller has some deviation to keep the system stable.And then,we study the robust stabilization problem for a class of uncertain discrete-time and time delays systems with fault conditions.Based on Lyapunov stability theory,the robust stability of discrete-time piecewise systems will be discussed.On the basis of this,the H_? performance index and l₂-l_? performance index of the system are analyzed,and the sufficient conditions for the system to stabilize and satisfy its performance are obtained.Select a appropriate fit the actual fault model to describe the fault part of the system,according to the H_? and l₂-l_? principles of robust and control,a robust H_? reliable controller and a l₂-l_? reliable controller design method for discrete-time and time delay systems with parametric uncertainties and actuator failures are given.And the results are transformed into a linear matrix inequality of the feasibility of the problem.And then through the numerical simulation to the design of the controller to verify.For a class of uncertain time-delay piecewise systems with sensor faults,this paper presents a robust and reliable filter design problem.First,The stability of the system isanalyzed according to the Lyapunov stability theory.Then,on this basis,we deduce the sufficient conditions that can make the system asymptotically stable and make the system meet the H_? performance and l₂-l_? performance constraints.Select a continuous fault model to describe the system failure to meet the actual engineering scenario.By applying the variable substitution method,the obtained nonlinear inequality is transformed into a linear matrix inequality that can be solved,and the filter parameters are solved.Finally,numerical simulation is used to verify the feasibility and effectiveness of the proposed algorithm.Finally,The piecewise system theory is applied in the CSTR system.Using the piecewise system to describe the dimensionless model.The reactor temperature is used as the standard of dividing the piecewise system.And then we design a H_? state feedback controller.Then the feasibility of the controller is verified by simulation.