Research Of Robust Control For Uncertain Time-delay Singular Bilinear Systems

The stability and the performance are concerned most in the control system. Uncertainty and time-delay phenomenon exist commonly in the practical application of the control system. They are two main factors, which destroy the system's stability and performance. In the recent years, uncertain and time-delay system is researched extensively by theoretical and practical workers. In order to maintain the system's stability and performance, the robust control attempts to describe the object's uncertainty and synthesize its controller within the perturbation scope permitted by the uncertainty. Robust control has become a hot issue of the control field. Singular bilinear system is a kind of singular nonlinear system which is most close to the singular linear system, and singular bilinear system models widely exist in the practical lives. Singular bilinear system can describe more accurately industrial objects on a large scale, which becomes a powerful tool for depicting the characterization of some practical systems. Therefore, the research of singular bilinear system has an important theoretical significance and practical application valueness.In this paper, based on the research condition of singular, bilinear, time-delay system theory, considering uncertain parameters in the two situations of the norm-bounded and meeting the matching condition, the robust control questions of uncertain time-delay singular bilinear systems are discussed. On the one hand, based on the theory of Lyapunov stabilization, the sufficient condition of stabilization for singular bilinear system with uncertainty and time-delay is presented by using the method of linear matrix inequality and applying the method of enlargement in the set domain simultaneously. On the other hand, the design method of a state feedback controller which makes the closed-loop system stable is illustrated. The main contents and results are summarized as follows.(1) The theory of uncertain time-delay normal system's robust stabilizatin is expanded to singular system. The two different uncertain time-delay singular system's robust control questions are discussed respectively. The sufficient condition of stabilization for singular system with uncertainty and time-delay is presented, and the design method of a state feedback controller which makes the closed-loop system stable is illustrated.(2) Regarding uncertainty in the different situations, two robust control questions of uncertain time-delay singular bilinear systems are discussed. One situation is that the uncertainty is norm-bounded; the other situation is that the uncertainty goes with the matching condition. The sufficient condition of robust stabilization for singular bilinear system with uncertainty and time-delay is presented, and the design method of a memoryless state feedback controller which makes the closed-loop system stable is illustrated. At the same time, through the LMI tool box, the effectiveness and rationality of the design methods are illustrated by the numerical examples.(3) For time-delay singular bilinear systems, where uncertainty is time-varying and goes with the matching condition, the sufficient condition of robust stabilization is presented in the LMI way, and the design method of a memory state feedback controller which makes the closed-loop system stable is illustrated.