Research On Stabilization For Switched Delay Systems

During the last decades, with the speedy development of social economy and scientific technology, there have been increasing research activities in the field of stability analysis and the switching stabilization problems of switched systems also have a lot research works. In the ideal case, the switching of the controllers coincides exactly with that of corresponding system modes, that is to say, the controllers are switched synchronously with the system modes. In actual operation, however, since it takes time to identify which subsystem is running and apply the controller which matches the subsystem, thus, there have time lags between the switching of the controllers and the switching of the subsystems, that is the switching time of controllers may lag behind that of practical subsystems, which results in asynchronous switching between the controllers and system modes. Due to the practicality and universality of the asynchronous switching system, the problem of asynchronous switching has become a very meaningful research subject. In a practical system, the state cannot be used for state feedback control system because they cannot be measured directly in some situations. It is very necessary to design the dynamic output feedback control for the stabilization of the system. Also, due to some external factors and the operation of the system itself needs time, it will lead to system time-delay phenomenon exists widely in engineering and social systems, which may cause instability or bad system performance in control systems. Therefore, the research for switched systems with time delay has important theoretical value and practical significance, especially for asynchronous switching system which has more general nature.This thesis mainly studies the following two aspects:(1) The problem of the stability and stabilization for a class of continuous time Markovian jump systems with time-varying delays and partly unknown transition probabilities are investigated. By considering the property that the sum of every element in each row for transition rate matrix is zero, a sufficient condition for the existence of state feedback controller is derived in terms of linear matrix inequalities by introducing a free-connection weighting matrix method and Lyapunov function. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.(2) The problem of output feedback stabilization for a class of switched neutral delay systems under asynchronous switching is considered. Asynchronous switching means that the switching of the controllers and the switching of the system modes are asynchronous. By constructing different Lyapunov functions in the match and mismatching running intervals for the controlled subsystems and controllers modes, and further allowing the Lyapunov function to increase in the mismatching running intervals, a sufficient condition for the exponential stability of the closed-loop systems is developed for the switched neutral system based on the average dwell time method, and the design method for output feedback controller is derived in the term of LMIs. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the proposed method.