| In the field of control system research,switched systems,many scholars have invested a lot of time and energy in the research of switched systems,due to its wide range of practical application and important scientific theoretical value.Switched positive systems,as a special type of switched systems,which have been widely used in many other fields such as medical,economics,industry,biology and so on.Since the switched positive systems contain both the complexity of the switched systems and the non-negative nature of the positive systems,the research work becomes more difficult,so the research on this system is full of challenges.First of all,As an important basic research problem of dynamic control systems,stability has become the focus and hot spot of most researchers.Secondly,the system will be affected by disturbances during operation.The study of the L1-gain performance of the switching positive system is particularly important in theoretical significance and practical application.So far,the research of switched positive systems has achieved certain results,but there are still many problems that need to be explored and solved.in this paper,a class of piecewise time-varying linear copositived Lyapunov functions is constructed,and based on the subsystem-dependent average dwell time switching signal,the stability criteria of the global uniform exponential stability and the unweighted L1-gain of the switched positive system are obtained.The research conclusions are as follows:First,in this paper,by constructing a class of piecewise time-varying linear copositive Lyapunov functions,the stability problem and L1-gain analysis of switched positive systems are discussed based on the mode-dependent average dwell time switching signal.Compared with the traditional multi-linear copositive Lyapunov function method,the proposed method discretizes the Lyapunov function that is satisfied by each subsystem at runtime,and uses interpolation to obtain piecewise continuous Lyapunov function,which greatly increases the flexibility.In addition,the subsystem-dependent average dwell time switching signal can ensure that each subsystem has its own average dwell time and has its own switching strategy,which reduces the conservatism of each subsystem for dwell time.Second,in this dissertation,the stability problems of switched positive systems with only stable subsystems,only unstable subsystems or both stable and unstable subsystems are discussed respectively,than,by constructing the piecewise time-varying linear copositive Lyapunov function,and utilizing the subsystem-dependent average dwell time switching signal,and adopting the switched strategy where slow switching and fast switching are respectively applied stable and unstable subsystems,the sufficient global uniform exponential stability condition for the system are presented.Then,the effectiveness of the proposed method is verified by numerical simulation.It is worth noting that,compared with the existing research methods,the research method in this paper can be applied to three types of system models simultaneously.Third,when the system is subject to external disturbances,by utilizing piecewise timevarying linear copositive Lyapunov function,and basing on the subsystem-dependent average dwell time switching signal,the L1-gain analysis is carried out for the switched positive system which are respectively consisted of only stable subsystem,only unstable subsystem and both stable subsystem and unstable subsystem,and a unweighted L1-gain performance index is obtained.Finally,the effectiveness of the method is verified by numerical simulation.It is worth mentioning that no scholars have explored the problem of unweighted L1-gain analysis in the study of the switched positive systems with both stable and unstable subsystems. |
