Event-triggered H_? Filtering Of Continuous-time Switched Linear Systems With OMI

Hybrid dynamic system is a kind of complex system composed of discrete dynamic events and continuous dynamic events.Since it was proposed,it has caused extensive re-searchin the field of automatic control in recent decades.Hybriddynamic system is a kind of multidisciplinary research problem.In the field of automatic control,hybrid dynamic systems are usually modeled as switching systems.The dynamic behavior of the switch-ing system is closely related to each switching subsystem and the corresponding switching signal.Due to some unavoidable factors,such as time delay,noise,non-linearity,etc.,the stability research of the switching system is complicated.At present,the stability anal-ysis of the problem of multiple switching between two sample instants under the event-triggered sampling mechanism and the design of the H_?filter are very limited.In real projects,complex asynchronous situations are very common.For example,when system resources are limited,the number of sampling instants becomes less,while switching can still be frequent.Thus,the H_?filter will mismatch the switching system during sever-val modal dwell time.Therefore,no matter from the theoretical research and practical engineering considerations,the research of this kind of problem is very important.The switching system is composed by a switching control signal and several switch-ing subsystems.Since proposed,it has caused extensive research in the field of automatic control in recent decades.Switching system is a kind of multidisciplinary fusion research problem.In the field of automatic control,its dynamic behavior is closely related to each switching subsystem and the corresponding switching signal.Due to some unavoidable factors,such as time delay,noise,non-linearity,etc.,the stability study of the switch-ing system is complicated.In order to make the output signal of the switching system smoother and reduce the influence of noise and disturbance as much as possible,the fil-ter is a good method to filter the signal.Considering the limited resource in the actual project,when the switching of the switching system occurs frequently,it is difficult for the filter to guarantee a high sampling frequency.Therefore,multiple switching occurs in the two sampling intervals,and the filter may not be able to match the system state of the switching system in multiple switching,which inevitably leads to a very complicated asynchronous situation.At present,the results of switching system stability analysis and H_?filter design for the problem of multiple switching between two sampling instant un-der the event-triggered sampling mechanism are very limited.Therefore,no matter from the theoretical research and practical engineering considerations,the research of this kind of problem is very important.This paper studies an event-triggered filtering error system composed of a switching system based on an event-triggered sampling mechanism and a H_?filter.The analysis of complex asynchronous conditions,system stability and H_?filter design are carried out.The work of this paper can be refined into the following aspects:(1)In order to reduce the influence of disturbance input and measurement noise in switchingsystem,this paperstudies the H_?filter to filter the outputsignal of the switching system,and proposes a filtering error system.In this system,the matching and mismatch-ing part between the filter state and the switching state,the ability to filter disturbance noise are described by the error function.Based on this filter error system,the complex asynchronous situation,event-triggered sampling mechanism,H_?filter design,system stability analysis,etc.are carried out respectively.(2)For resource-constrained conditions orwhen the system is frequently switched,the sampling instants are less than the switching instants,multiple switching occurs between two adjacent sampling instants.In this case,the filter may not be able to match the system state in the several modal dwell time,and the asynchronous time will be greater than the modal dwell time.The asynchronous time periods caused by multiple switching may overlap within each other to form overlapping asynchronous time intervals.Aiming at this kind of complex asynchronous situation,this paper constructs mathematical models for all synchronous and asynchronous situations separately,so as to simplify the analysis of complex asynchronous situations.(3)The event-triggered sampling mechanism is used to replace the traditional time-triggered sampling mechanism.Under this mechanism,sampling will be triggered only when the system error meets certain conditions.The traditional time-triggered sampling mechanism will cause a lot of unnecessary sampling,which greatly wastes system re-sources.Event-triggered sampling,a flexible sampling mechanism that fits the hypothe-sis of this paper,can greatly reduce the number of samples and only keep the necessary samples.(4)Based on the continuous-time linear switching system and the filter system,the filter error system is derived.In view of the assumption that multiple switching between two sample instants is allowed,combined with multiple Lyapunov energy functions,the mathematical model underthis assumption is given,and the stability result ofthe switching system and the design of the H_?filter are given.The modal dwell time criterion and system L₂gain analysis are presented.The coefficients of the filter are solved by a series of linear matrix inequalities.In order to use the LMI toolbox in Matlab,a relaxation matrix Q is introduced to separate the unknown variables to be solved,so that the linear matrix inequality solution method is used to obtain Filter coefficients and coefficients of the event-triggered sampling mechanism.(5)A numerical simulation example is used to prove the validity of the conclusions of this paper.At the same time,a comparison with the conclusions in the existing articles proves the innovation of this paper.