The Finite-Time Stability And Passive Control Of Singular Systems

In this paper, taking advantage of the Lyapunov function、 linear matrix inequalities and the magnified inequalities, the problems of the finite-time ro-bust passive control, observer-based robust passive control for uncertain singular systems and observer design for discrete-time singular systems are studied. The main results obtained are showed as follows:(1) Aiming at a class of uncertain time-delay singular systems with external disturbances, the problems of the finite-time robust passive are discussed. Firstly, according to the Lyapunov function and the linear matrix inequality, the suffi-cient conditions of the finite-time stable and robust passive for the open-loop nominal systems are given. Secondly, by introducing new matrix variables, the sufficient conditions proposed are used to prove the existence of state feedback controllers. And the controllers guarantee that the closed-loop systems are the finite-time stable and robust passive, under the environment of arbitrary delay and all admissible uncertain parameters. And the parameters of controllers are provided.(2) Pointing at a kind of uncertain time-delay singular systems with exter-nal disturbances, the problems of the observer-based robust passive control are considered. First, in view of the Lyapunov function and magnified inequalities, the sufficient conditions given in form of matrix inequalities guarantee the closed-loop systems be asymptotically stable and robust passive. Second, with the Schur complement and linear matrix inequalities, the sufficient conditions proposed are used to certify the existence of state observer, and the gain matrix of the observer is provided.(3) Aiming at a category of discrete-time nonlinear singular systems with time-delay, the problems of observer design are researched. First, when the states are not completely available, on account of the Lyapunov function and li-near matrix inequality, the sufficient conditions proposed to testify the error sys-tems be asymptotically stable are given. The representation of gain matrix of state observer is provided. Second, similarly, the methods of obtaining sufficient conditions to guarantee error systems be asymptotic stability are extended to the systems with uncertain parameters.The feasibility and the effectiveness of the proposed methods are showed by numerical examples.