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Study Of Stability Analysis And Related Control Problems For General Periodic Descriptor Systems

Posted on:2008-08-31Degree:MasterType:Thesis
Country:ChinaCandidate:G WangFull Text:PDF
GTID:2178360215961661Subject:Control theory and control engineering
Abstract/Summary:PDF Full Text Request
In recent years, as the study for descriptor system goes deeper and deeper, marvelous research results have been achieved. Descriptor system has become one of the independent embranchment of the modern control theory. While most of the research results are mainly focusing on invariable descriptor systems and the research results on the periodic descriptor systems are comparable few. The research results are especially few for the general periodic descriptor systems. One of the reasons is that the general periodic descriptor system is more complex than the periodic descriptor systems. The main difference between periodic descriptor systems and general periodic descriptor systems is that periodic descriptor systems' Jacobian matrix is constant matrix. While the general periodic descriptor systems' Jacobian matrix is periodic time-varying matrix, which brings some trouble for the research work on the general periodic descriptor systems, hence the research results on the general periodic descriptor systems are comparable few. This thesis studies on the stability and the related control problems for the general periodic descriptor systems. In this thesis, normal periodic liner systems, robust control theory and H_∞control theory are combined here, the Lyapunov method and LMI are adopted, to make deep and profound research on the stability and the related controlling problems of general periodic descriptor systems. The main contributions are as follows:(1) For the general periodic continuous singular systems, the necessary and sufficient condition was presented for impulse-free and asymptotic stability of general periodic singular system by establishment of generalized Lyapunov inequality. Based on this work, the necessary and sufficient condition for the systems to be quadratic admissibility was also studied and the controller design method was given. These results are useful for further investigation of singular general periodical systems.(2) For linear uncertain general periodic descriptor systems, the necessary and sufficient condition of robust stability was presented, and a kind of state feedback robust controllers was given. Then, the relationship between quadratic stability and robust stability of the systems was discussed.(3) For the general periodic continuous singular systems, the generalized Lyapunov inequality and LMI are established. H_∞control problem is discussed for general periodic descriptor systems without control input, a necessary and sufficient condition is obtained for this kind systems to be admissible and satisfy performance index of H_∞control. Finally, the state feedback is introduced, then an tribe solutions of state feedback H_∞controllers for linear time-varying general periodically descriptor systems are obtained.
Keywords/Search Tags:General periodically time-varying descriptor systems, Lyapunov inequality, Admissibility, Robust stability, H_∞control
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