The Solution To Descriptor Systems And Its Application

Because descriptor systems are much more complex than the standard state systems, their related solution algorithms are much more difficult and complex. Though related solution algorithms of descriptor systems play an important role in their research and development, their general algorithms are not perfect and mature. Hence, It is meaningful to study the general solution algorithms. This thesis make a thorough research about general solution algorithms, the main contribution of this paper is summarized as follows:(1) The main background of the problem discussed in this thesis is introduced. This thesis mainly introduces the background of the research about descriptor systems theory and solution algorithms, which is primary about the LMIs with equality constraints and solutions of the generalized Lyapunov matrix equation. In addition, the development and application of the LMI are presented.(2) The fundamental knowledge and some important theorems and lemmas cited in this thesis are concisely offered.(3) Some general solution algorithms of some matrix equations in descriptor systems are presented. The general solution algorithms of the generalized Lyapunov matrix equation are presented with the Kronecker product and LMI method. This thesis also derives the general solution of the generalized Lyapunov-like matrix equations with singular value decomposition. Then the general solution of the equality constraints is presented.(4) The general solution and method of the LMI with equality constraints is presented and applied to the controller design of stability, stabilization, robust control, H∞control, delay systems and so on. This thesis also gives the general solution algorithm of the LMI with equality constraints with the semi-definite programming method.(5) A summary of this thesis is given. At the same time, we give an expectation for the future work. As to the conclusions obtained in the thesis, simulation examples are presented to show the usefulness and effectiveness of the proposed methods.