Finite-time Stability And Stabilization Of Singular Systems

Based on Lyapunov stability theory, linear matrix inequality and restricted equivalent forms, the finite-time stability and stabilization are discussed in this thesis for systems with exogenous disturbances, including discrete-time singular systems, uncertain discrete-time singular systems and the linear singular systems. The state feedback controller is designed. The main contents are as follows:1. By means of Lyapunov function and linear matrix inequality, the finite-time stability and stabilization are studied on a class of discrete-time singular systems with norm-bounded exogenous disturbances. First, the sufficient conditions of the finite-time boundedness are given for discrete-time singular systems with exogenous disturbances under the state of no feedback controller. Then, the state feedback controller and the output feedback controller of the discrete-time singular systems with exogenous disturbances are proposed, so that the closed loop systems are finite-time bounded. Last, the effectiveness of the proposed method is illustrated by a numerical example.2. By using Lyapunov function and linear matrix inequality method, the finite-time stability and stabilization are studied on a class of uncertain discrete-time singular systems with norm-bounded exogenous disturbances. First, the sufficient conditions of a class of uncertain discrete-time singular systems with finite-time boundedness are given. Then, the finite-time stability of closed loop systems via static state feedback controller is studied. The sufficient conditions of finite-time boundedness are given for the uncertain discrete-time singular systems with exogenous disturbances. Last, the proposed method is illustrated by a numerical example.3. According to a kind of linear singular systems with exogenous disturbances, a new definition of the singular systems with finite-time stability is given based on the convex polyhedron region. Then, the sufficient conditions of the open loop systems with the finite-time stability are provided. The finite-time stability and stabilization of the closed loop systems via static state feedback controller are studied. Meanwhile, a method is given for designing the state feedback controller.