Resarch On Robust Control Method For Linear Switched Systems Based On PDT

Switched systems,as one of the special and important branches of hybrid systems,are composed of two or more subsystems and a switching law that specifies the activation order of subsystems.This special system structure makes the switched system have multiple modes and allowed to have multiple controllers,so it has the ability to model complex physical objects and then provides a simple and effective research method for dealing with the analysis and control synthesis of hybrid systems.However,the existed theoretical results for switched systems are still insufficient.Most of the time-dependent switching laws focus on dwell-time switching law and average dwell-time switching law.There are relatively few research results on the persistent dwell-time switching law with higher design freedom and stronger description ability of fast switching.On the other hand,passivity,as a special form of dissipativity,is widely used in system analysis and synthesis.As an effective tool to study passivity,the energy storage function can also be used as a candidate function of Lyapunov function,which shows that it can not only ensure the passivity of the system,but also ensure the stability of the system.Therefore,the control based on passivity is also an important topic in the field of system synthesis.However,in the existing research on passivity and feedback passification of switched systems,most of the designed controllers are full-order or based on system model reduction,which is conservative.Therefore,based on the existing results,this paper will further discuss the robust control,passivity and reduced-order feedback passification of linear discrete-time switched systems under mode dependent persistent dwell-time switched signals.The main research contents of this paper are as follows:The problem of robust control for a class of linear discrete-time switched systems is studied.Considering the fast switching of the switched systems,one more general persistent dwell-time switching law is adopted,and the performance redundancy generated by slow switching is used to compensate the performance degradation caused by fast switching,so as to finally make the system stable.In addition,based on the proposed switching law,a time varying state feedback controller is designed for the first time,which can change the controller gain according to the real-time state of the system,so that the closed-loop system has robust stability and minimum l₂gain.The output feedback robust control problem for a class of linear switched systems is discussed.Considering the performance differences among the subsystems,a more advantageous mode-dependent persistent dwell-time switching law can be used to design time-varying controllers according to the characteristics of the subsystems and to improve the freedom of switching signal design.In addition,considering that some of the states of a type of switched system can be directly measured,a reduced-order feedback controller is designed accordingly,which can reduce the amount of computation while improving the robustness of the closed-loop switched systems.Passivity and output feedback passivation of linear discrete-time switched systems are addressed.When the state part of the system is measurable and no subsystem is passive,the strict passivity condition and the non-weighted passivity index of the closed-loop discrete-time switched system under the model-dependent dwell-time switching law are obtained by introducing a time-dependent energy storage function.Secondly,a reduced-order output feedback controller with time-varying gain is designed,which ensures the passivity of the closed-loop system and solves the feedback passification problem of the closed-loop discrete-time switched system by using some of the system measurable states and time-varying parameters describing the mode-dependent persistent dwell-time.Finally,a summary of the graduation thesis is provided,and some suggestions on the development trend of this subject are put forward.