Multi-rate Sampled-data Control Of Switched Linear Systems

With the rapid development of computer technology and digital signal technology,digital control system has been widely used in the fields of national defense construction,livelihood,scientific research and so on.However,in the research on the practical application of sampled-data control system,some practical problems are often neglected.For example,the change rate of the controlled object different signals are large,and it is unrealistic to require the same sampled-data rate.Sampling period selects the general assembly affects the performance of the system,too small will increase the cost of the system.A compromise method is to use different sampled-data rate of the system's different signal,that is,multi-rate sampled-data control.Considering the fact that many systems can be modeled as switching systems,switching systems are also a very important research topic in the field of control.Therefore,it is very practical to study the multi-rate sampled-data control of switched systems.In this paper,based on the research of multi-rate sampled-data control,the stability and controller design of the switched system under multi-rate sampled-data control are analyzed.The main contents are as follows:The practical stability problem of a switched affine system under multi-rate sampled-data control is studied.The state component is sampled in uncertain aperiodic sampling through different sensors.When the equilibrium point of the system is not unique,a new single Lyapunov functional and a switched Lyapunov functionals with state component sampling information are constructed by considering whether the system has a stable convex combination.The practical stability of the whole system is ensured by the design of state-dependent switching rules.The exponential stability of a linear switched system under multi-rate sampled-data control is discussed.By designing event-triggered scheme for each state component,constructing a class of functions composed of multiple Lyapunov functional and closed loop auxiliary function,the sufficient condition of sampling state feedback exponential stabilization for switched system is obtained,and the design of sampling controller and state dependent switching law is carried out.The exponential stability problem and H_?control performance of uncertain linear switched systems with external disturbances under multi-rate sampled-data control are studied.A new event triggered mechanism based on each subsystem partition is designed.Under the given assumption,based on the functionals composed of multiple Lyapunov functional and closed-loop auxiliary functions,a multi-rate sampled-data controller and a state-dependent switching law are designed for the system with external disturbances and uncertainties.And the H_?control performance level is given.The sufficient conditions for exponential stability of uncertain linear switched systems under multi-rate sampled-data control are obtained.