Pole Placement And Robust Controller Design For Switched Positive Linear Systems

As an important class of hybrid systems,switched systems consist of a family of subsystems and a rule orchestrating the switching among them.Switched systems are widely used in the engineering practice because of their unique characteristics,and they have a good effect on solving complex system problems.In recent years,with the development of switched systems and positive systems,switched positive linear systems(SPLSs)have attracted the attention of many researchers,and they have been widely used in the networks,communication systems,formation flying and infectious disease.SPLSs possess both the complex dynamic behavior of switched systems and the unique properties of positive systems.Therefore,studying such systems has important theoretical and practical value.In this thesis,we mainly study the stabilization problems for some kinds of SPLSs.Our objective is to design controllers and combine the corresponding switching strategy to achieve stability of the closed-loop systems with the performance improved.The main work of this thesis is summarized as follows:First,we study the problem of regional pole placement for positive systems.We obtain the feasible region for spectra of positive systems and present the design method of the regional pole placement controller.Second,for time-delay SPLSs with structural uncertainty,we design robust controllers.We design the state feedback controller by using multiple Lyapunov-Krasovskii functional method,which guarantees that the closed-loop systems are positive and have a weighted H? performance under average dwell time switching signals,at the same time every subsystem is D-stable.Third,the bounded controller is designed for time-delay linear interval switched positive systems with constraint control.We design the state feedback controller to guarantee that the closed-loop systems are positive and stable under arbitrary switching signals,at the same time the controller is bounded under certain conditions.The conclusions and perspectives are provided in the end of this thesis.