H_∞Filtering For Discrete Time Switched Systems With Missing Measurements

In the past few decades, many of dynamical systems encountered in practice are of hybrid nature, so it has attracted a lot of attention in the control field. Switched system is one of the most important systems which not only contains a family subsystems but also has a switching rule which decides the schedule of those subsystems. In general a switching rule may be state dependent or time dependent or a combination of them. In practical applications such as target tracking, the measured output may only contain noise or not contain completely useful signals if the target is absent. Similarly, in the cases of sensor temporal failure, network transmission delay or loss, sensor energy limited suspend working temporarily and so on, the measured date will be lost, therefore the filtering problem with missing measurement is meaningful. Moreover the subsystem is activated by the switching rule, then the corresponding filter activated, so the switching instant of filter exceeds or is delayed behind that of the corresponding subsystem, in other words asynchronous switching is happened between the subsystem and the corresponding filter. We study about these situations.The main research works in the thesis are as follows:In chapter1, the theoretical and practice significance of thesis is introduced and the international and domestic research situation of thesis is summarized.In chapter2, is discussed the problem of robust H∞filtering for discrete time switched systems with missing measurement. All of subsystems are unstable. We partition the whole state space in different region which make every subsystem exist a Lyapunov-like function in a certain region. The state-dependent switching rule is structured by the largest region function strategy. By using the S-Procedure which transform these constrained matrix inequality into linear matrix inequality and multiple Lyapunov functions approach, sufficient conditions of exponentially stable in the mean square are obtained for nominal filter error system and parameter uncertain filter error system respectively. Then by introducing some slack matrix variables, design the corresponding H∞filter for nominal systems and parameter uncertain systems. Finally the efficiency of the proposed approach and results are validated through a Matlab/Simulink tool.In chapter3, the problem of H∞filtering for discrete-time switched linear systems with missing measurement under asynchronous switching is investigated. Two sensors are used to measure the system output meanwhile the missing measurement is considered, the switching between filter and the correct subsystem is not synchronized. Under the given switching rule, the filter error system is exponentially stable in the mean square by average dwell time and switched Lyapunov function approach. In addition the filter parameters can be obtained by solving a set of linear matrix inequalities. Finally the proposed approach and results is valid by an mumerical example.In chapter4, the main research works of the thesis are concluded, and some research issues in future are prospected.