The Finite Time Stability Of The Uncertain Discrete Generalized Switched Systems

Because of the structure of the generalized system is complex, so it is more difficult for research than the normal system, and more complex in the analysis and design of the system. In this thesis, the generalized discrete switched system is researched. In the research of the finite time stability of generalized discrete switched systems with external disturbances and uncertain discrete-time singular switched systems with external disturbances, Lyapunov stability theory and the linear matrix inequality is used. The main research contents of this thesis are as follows:1. According to the generalized discrete switched systems with external disturbances, the finite time stability of the system is researched by using the method of Lyapunov function and linear matrix inequality method. Firstly, in the absence of state feedback, sufficient conditions of finite time boundedness of the generalized discrete switched systems with external disturbances are given. Secondly, the design method of the state feedback controller of the discrete switched singular systems with external disturbance is presented. Finally, the design method of state feedback controller design method is proposed for reference, then, the output feedback controller of discrete singular switched systems with external disturbances is proposed.2. For the uncertain discrete generalized switched systems with external disturbances, the finite time stability of the system is explored again with the method of Lyapunov function and linear matrix inequalities. First, the sufficient conditions of finite time boundedness are given for uncertain discrete singular switched systems. Then the design method of the state feedback controller of the system is proposed.