Singular system is a kind of dynamics of more general from compared with state-space systems. Recently the singular system with time-delay is frequently encountered. So it has a wide practical background the studies of time-delay systems. Because the existence of time-delay is often the reason of instability the control performance. In fact, passivity is a kind of stability of a higher level of general. Usually we often need to construct a Lyapunov function to stabilize a system. This process can be transformed into a storage function of passivity. Therefore, the passivity theory plays an important role in the stability analysis of control system So the analysis of delay-dependent stability and the passive control problem is always the major research topic in the field of control. Aiming at the problem of delay-dependent passive control, Based on the existing results, further discusses the delay-dependent stability constant time-delay singular systems, based on Lyapunov stability theory, through using the method of linear matrix inequality and free weighting matrices, obtained by considering the delay dependent stability condition of the system.Based on the above, this thesis uses the method of integral inequality and free weighting matrices discussed the delay dependent stability of linear singular systems with delay is passive control related problems, the main contents are as follows:(1) The main background of the problem discussed in the thesis is introduced completely. Firstly, the stability of singular systems research methods is summarized and the analysis of their applicable scope. Then the free-weighting matrices are introduced. Further, the significance and the recent progress are presented for the theory of passive. At the same time, the basic characteristics of main methods used to handle delay-dependent passive problem are reviewed about singular systems, so is the main method. Finally, the main word this paper is summarized.(2) The related of knowledge LMI is introduced, the application of Schur and three kinds of standard problems. Then the related of theory about singular system is introduced, in particular, admissibility of singular system and restricted equivalent transformation, the behind of Time-Delay Singular system’s solving and transforming provide a solid theoretical basis. The main lemma is introduced in the paper (the general form to special form) and it also proves the relate of lemma.(3)This chapter using delay segmentation method combining Jensen inequality, the delay dependent stability condition of generalized time-varying systems with time delay. The Lyapunov approach is used by combining the integral inequality with the free-weighting matrices. No model transformation is employed. The corresponding conclusions are extended to multiple time delay singular systems. For a system with time delays, delay-dependent criteria are derived by choosing Lyapunov function, which one special double integral term is about the relationship between the delay hi and hj. In this way the conservative of the system greatly reduced. Numerical examples demonstrate that the method used in this chapter is relatively simple.(4) The delay-dependent passive control for linear singular system with delay is discussed. The Lyapunov approach is used by combining the integral inequality with restricted equivalent transformation.Then the design of two types of controller is presented for the closed-loop systems to be the delay-dependent stabilization condition. The numerical examples demonstrate the method is entirely based on the LMI state feedback controller design. Do not have to adjust any parameters any iterative processing.(5) A summary of this thesis is given. At the same time, we give a prospection for future work. |