The Finite Time Control Of Discrete Singular Systems

In the analysis and design of control systems, the stability is the first problem that people consider and need to solve, especially for the asymptotical stability. Usually asymptotical stability can satisfy the needs of the control project. It de-scribes the steady-state behavior of the systems, but can’t describe the transient performance. Sometimes, there could be a system which is asymptotically stable, but it has very bad transient performance. Therefore it plays a terrible influence on the pratical project. Worse more, it even can’t be applied. In order to research the transient performance of the systems, Peter Dorato put forward the concept of short-time stability in1961, which is now called finite-time stability. The finite-time stability is referred to that in the finite interval the path of the state can’t exceed the given bounds. It is different from the concept of stability under usual conditions. Because of the rapidity and accuracy of the finite-time control, it will be a new and broad research field in the control theory.The main conclusions in this paper are as follows:(1)The cocepts of finite-time stability and finite-time boundedness are given. Some sufficient conditions are found,which can guarantee the existence of controllers and stabilize the closed-loop systems. By the solving of linear matrix inequalities, the design of controllers is proposed. Then, two numerical examples are given to demonstrate the effectiveness of the approach.(2)The cocepts of finite-time robust stability and finite-time robust bound-edness are given. Some sufficient conditions are found.which can guarantee the existence of controllers and stabilize the closed-loop systems. By the solving of lin-ear matrix inequalities, the design of controllers is proposed. Then, two numerical examples are given to demonstrate the effectiveness of the approach.