Stability Analysis And Design For Some Classes Of Nonlinear Descriptor Systems

Descriptor system is a class of systems described by differential equations and algebraic equations, which has wide areas such as aerospace, chemical engineering, biomedical, energy, network, power, economy, communication and so on. Stability as a basic protection of normal operation of the system has been a research focus of descriptor systems. This thesis investigates the problems of Lagrange stability and input-state stability (ISS) by using Lyapunov stability theory and linear matrix inequality (LMI) etc.The main contribution of this thesis is summarized as follows:(1) The main background of the problem discussed in this thesis is introduced. Firstly, the structure characteristics and recent progress for singular systems are introduced. Then the significance and recent progress are presented for Lagrange stability and input-state stability (ISS), furthermore, the significance, application background and the recent progress are presented for Lagrange stability and input-state stability (ISS). At the same time, the main frame and main method are presented. Finally, the main work this thesis is summarized.(2) The mathematical definitions for Lagrange stability and input-state stability (ISS) in this thesis as well as restricted equivalent transformation of generalized systems are introduced, which are in preparation for later proved. Then some concepts and conclusions cited in this thesis are also concisely offered.(3) In this paper, Lagrange stability is addressed for a class of nonlinear descriptor systems. First, some sufficient conditions for Lagrange Stability of nonlinear descriptor systems are derived, which generalizes the existing Lagrange stability criteria for normal systems. Furthermore, by using descriptor system theory, linear matrix inequality based analysis methods are given. Finally, Chua’s oscillator circuit is analyzed by using the proposed methods, which demonstrates the effectiveness of the proposed methods.(4) Input-state stability (ISS) of Lur’e descriptor systems (LDS) with disturbances is investigated. Firstly, the notion of input-state stability (ISS) for nonlinear descriptor systems is defined based on the concept of ISS for normal systems and the characteristics of descriptor systems. Then, an LMI-based sufficient condition for ISS of LDS is derived by the classical ISS theory.(5) A summary of this thesis is given. At the same time, we give an expectation for the future work. As the conclusions obtained in the thesis, simulation examples are presented to show the feasibility and effectiveness of the proposed methods...