Filter Design Of A Class Of Switched Systems

In the last two decades, hybrid systems have attracted a recurring interest in the control community for they exist widely in engineering and social systems. Among various kinds of hybrid systems, switched system is the most typical one. Switched systems consist of a family of continuous-time or discrete-time subsystems and a switching law, which defines a specific subsystem being activated during a certain interval of time. This work, which is supported by the National Natural Science Foundation of China, investigates the problem of filter design for switched systems by applying Lyapunov functions theory and average dwell time approach. The main contributions are as follows.The robust H∞filtering problem for a class of continuous-time linear and nonlinear time-delays switched systems which satisfy Lipschitz conditions are investigated, based on piecewise Lyapunov functions theory and average dwell time approach, the condition that guarantee the filtering error system to be exponentially stable with a prescribed H∞performance is derived, and the existence conditions of linear filter are proposed in terms of LMI.It is considered that in practical application, there exists asynchronous switching between the filter and the system, that is, the real switching instants of the filter will exceed or lag behind those of the system, we study the robust L2-L∞filtering problem for continuous-time switched linear systems under asynchronous switching. By using piecewise Lyapunov functions theory and average dwell time approach, and combining the stability analysis idea which is used to deal with the switched system with stable and unstable subsystem, then the filter parameter expression is derived.We consider the problem of the robust l2-l∞filter design for discrete-time switched time-delay systems with missing measurements. The missing measurement means that the system's measurement output is not consecutive but contains missing observations. The objective is to design a linear filter to guarantee the filtering error system exponentially mean-square stable for a prescribed noise attenuation level in the l2-l∞sense and missing measurements probability. By using piecewise Lyapunov functions and average dwell time approach, a sufficient condition on the existence of filter is given in terms of LMIs.The problem of robust H∞filtering for discrete-time switched time-delays systems with missing measurements and asynchronous switching is investigated. According to the piecewise Lyapunuov function and average dwell-time approach, we propose the sufficient condition for the existence of exponentially mean-square stable for the filtering error system also H∞performance is analyzed, and the solution of the desired filter parameters has been formulated in terms of a set of LMIs.