Control And Filtering For 2-D Discrete Switched Systems With Known Sojourn Probabilities

In recent years,the automation of the control systems is higher and higher,the function of the systems is mightier and mightier,and systems are becoming more and more complex.With the further research of some systems,the description method of onedimensional(1-D)state variables is extended to the two-dimensional(2-D)systems.Among the study of 2-D systems,2-D discrete switched systems are very special,for these systems,which embody the switching characteristics among subsystems,take the external conditions and control objectives into account,and switch to different modes at run time.When analyzing most of the switched systems,the elements of the switching rules need to be known in advance.However,in practice,it is very difficult to get all these elements about the switching systems,so that a new switching rule which are easier to be measured is needed.Actually,in addition to the transition probabilities,the sojourn probabilities can also be used to the study of switched systems.On the one hand,the sojourn probability information can be obtained by the numerical algorithm simply.On the other hand,some problems,such as random pocket loss and electronic components faults,may occur in some systems,and these systems can be expressed by switched systems with sojourn probabilities.The concept of sojourn probabilities has been used in 1-D switched systems in some of the literature.Hence in this paper,we mainly study on the control and filtering problems of 2-D discrete switched systems with known sojourn probabilities.In this paper,the background and the significance of the research are given at first,followed by the summary and the analysis of the current research situations.The main body of this research is mainly divided into three parts.In the first part,the concept of sojourn probabilities is extended to 2-D switched systems.The modeling and performance analysis of the system are carried out,and the sufficient conditions for the systems to be asymptotically mean square stable and satisfy the given ? performance index are obtained.The analysis result is then used into the design of the state feedback controller.A theorem is given to guarantee the mean square stability and the given performance of the closed loop system.Finally,the effectiveness of the proposed theorem is proved by giving a numerical example.The second part designs an output feedback controller for the 2-D discrete switched system with known sojourn probabilities based on the analysis results.A numerical example is presented to illustrate the effectiveness of the designed controller.In the third part,the filter of the 2-D discrete switched system with known sojourn probabilities is designed.Firstly,the filtering error system is obtained.Then the condition that satisfy the mean square stability and the given performance index is derived.Finally,a simulation example is given to verify the correctness of the design.The last part of the paper is the conclusion.It summarizes the main research contents,points out the innovation and the remaining problems of the research,and raises prospect for the research in the future.