Stability And Passivity Analysis And Synthesis Of 2-D Switched Continuous-discrete Systems

2-D continuous-discrete systems propagate information in two directions.According to whether the information propagation is discrete or continuous in two directions,2-D systems can be divided into 2-D discrete systems,2-D continuous systems and 2-D continuous dis-crete systems.Compared with 2-D discrete systems,2-D continuous-discrete systems have less achievement due to system complexity.Since 2-D continuous-discrete systems have many prac-tical applications in repetitive processes,iterative learning control,vehicle platoon control and channel irrigation,they have received wide attentions.In practical problems,systems may be required to switch in different subsystems,the introduction of switching law makes the dynamic behavior of the systems more complex,so the research of 2-D switched systems has become a new hot spot.In this paper,attentions are focused on the stability and passivity analysis and control of 2-D systems.The main research works of this dissertation are stated as follows:1.The stability of 2-D switched continuous-discrete systems is studied.By designing a state dependent switching law that only relies on time,the stability conditions of 2-D switched continuous-discrete systems are obtained.Then they are applied to the switched repetitive pro-cess modeling by 2-D switched continuous-discrete systems,and the sufficient conditions for the stability along the pass of switched repetitive process are obtained.The H? performance of switched repetitive process is discussed,and a feedback H? controller is designed to ensure the closed-loop systems' stability along the pass under a disturbance attenuation level.2.The passivity of 2-D switched continuous-discrete systems under the state dependent switching law that only relies on time is discussed,and the passivity sufficient conditions are obtained.When there is an external disturbance in 2-D switched continuous-discrete systems,passive filters based on observer and general form are designed to ensure the passivity of closed-loop 2-D switched continuous-discrete systems with exogenous disturbance.3.The passivity of a class of nonlinear 2-D switched discrete-time systems is studied.By introducing the concept of passivity of this class of systems on triangle area,a state dependent switching law is designed to ensure the passivity of linear and nonlinear 2-D switched sys-tems without the requirement of passivity of subsystems.When the states of the systems are completely measurable,state feedback controllers for the nonlinear 2-D switched discrete-time system is designed to make the closed-loop system passive.The output feedback controller of linear 2-D switched discrete-time systems with partially measurable state is given to ensure the passivity of the closed-loop system.Finally,based on the stability criterion of the frequency domain,sufficient conditions in a new linear matrix inequality(LMI)form for the stability of 2-D discrete systems are proposed,improved by frequency-partitioning approach,the obtained sufficient conditions have less conservatism.4.The finite time stability and finite time boundedness problems of 2-D continuous-discrete systems are considered.By using mathematical induction,a iterative formula of system states is established,then the LMIs criterions of finite time stability and finite time boundedness of 2-D continuous-discrete system are derived.The state feedback controller is further designed and the finite time stabilization problem of the systems is solved.The numerical simulations are carried out in the end of every part to verify the validity of the results.