Dynamic Output Feedback H_∞ Control For Discrete-Time Linear Switched Systems With Frequent Asynchronism

The objective of the study is discrete-time linear switched systems,which have been widely studied by researchers in the automation field since its inception and have sig-nificant practical value in engineering practice.Switched systems generally consist of multiple subsystems,and the switching process of the system is the process of switching between these subsystems.In actual engineering practice,due to limited resources,the controller cannot maintain a high sampling frequency.Therefore,when the subsystems switch frequently between two sampling instants,it can lead to a mismatch between the system state and the controller,resulting in complex asynchronous switching situations.In addition,there is also noise interference in the environment,which makes the stabil-ity analysis of the system very complex.In order to simplify the analysis process,some research has allowed the controller to directly sample the system state.However,in engi-neering practice,the complete information of the system state is not always directly avail-able,so this article considers using dynamic output feedback control.Currently,there are limited results for the stability analysis of linear switched systems under event-triggered mechanisms that allow frequent switching between sampling intervals and their corre-sponding dynamic output feedback H_∞controller design.Therefore,whether it is for the sake of expanding theoretical boundaries or for practical engineering considerations,re-search on these types of problems is very necessary.This article studies a design scheme for the dynamic output feedback H_∞controller of a discrete-time linear switched system based on an event-triggered mechanism.The switched system undergoes complex stabil-ity analysis,l₂gain performance analysis,and corresponding controller design.The main research content of this article can be subdivided into five parts:（1）In order to reduce the data communication volume of the system,this article adopts an event-triggered sampling mechanism instead of the traditional periodic sam-pling mechanism.Under the event-triggered sampling mechanism,sampling behavior is triggered only when the error satisfies certain conditions.This reduces the number of samples when the switching is infrequent and increases it when the switching is frequent,thus greatly reducing the data communication volume while ensuring the stability of the system.（2）The complex asynchronous situation caused by the frequent switching of subsys-tems during controller sampling intervals is considered.In order to be closer to engineer-ing practice,this article does not limit the minimum dwell time of subsystems,so it is possible for subsystems to switch frequently between controller sampling intervals.This will make the synchronization and asynchronous switching of the system more compli-cated.In the stability analysis of this article,these situations are classified and discussed.（3）For a type of discrete-time linear switched system based on an event-triggered mechanism,this article uses the multiple Lyapunov energy function method and the av-erage dwell time method to analyze its stability and weighted l₂gain performance based on the analysis of asynchronous situations.Compared with the single Lyapunov energy function method,the multiple Lyapunov energy function method reduces conservatism and can more accurately approximate the energy states of each subsystem.The average dwell time method is more widely used in practical applications because it does not limit the minimum dwell time of subsystems.（4）The dynamic output feedback H_∞controller and corresponding event-triggered mechanism parameters are designed based on stability conditions.After obtaining the stability conditions,this article combines various mathematical tools to deal with the cou-pling item problem in the stability conditions and obtains several solvable linear matrix inequalities,thus providing mathematical basis for controller design.（5）The effectiveness of the conclusions of this article is demonstrated through a numerical example.Additionally,the compatibility between event-triggered and periodic sampling mechanisms is discussed.