Abstract
This paper is concerned with sampled-data controller design for singular systems with time delay. It is assumed that the sampling periods are arbitrarily varying but bounded. A time-dependent Lyapunov function is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Combining input delay approach with Lyapunov method, sufficient conditions are derived which guarante that the singular system is regular, impulse free, and exponentially stable. Then, the existence conditions of desired sampled-data controller can be obtained, which are formulated in terms of strict linear matrix inequality. Finally, numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.
Highlights
In the last decade, considerable attention has been devoted to sampled-data control systems, because modern control systems usually employ digital technology for controller implementation [1,2,3,4,5,6,7,8]
It should be mentioned that the problem of sampled-data exponential stability of singular systems with time constant delays and uncertain sampling is solved in Theorem 8, and sufficient conditions of the existence of the desired sampled-data controllers are given, which are formulated by LMIs and can readily be solved by standard numerical software
Under the above gain matrix, the response curves of system (5) are exhibited in Figure 2, which shows that the states are tending to zero; that is, singular system (5) can be stabilized by the proposed sampled-data controller
Summary
Considerable attention has been devoted to sampled-data control systems, because modern control systems usually employ digital technology for controller implementation [1,2,3,4,5,6,7,8]. The time-dependent Lyapunov functional method has been applied to all sorts of sampleddata systems, and some useful results have been obtained (see, e.g., [17,18,19,20,21,22,23,24] and the references therein). Abstract and Applied Analysis information about the actual sampling pattern, and (3) how to design a set of easy-to-implement sampled-data controllers in order to guarantee that the singular systems are exponentially stable. It is, the main aim of this paper to challenge the sampled-data control for singular systems by overcoming the aforementioned three major difficulties. For a symmetric matrix, “∗” denotes the matrix entries implied by symmetry
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