【作者】 吕明珠；

【导师】 苏晓明；

【作者基本信息】 沈阳工业大学 ， 控制理论与控制工程， 2006， 硕士

【摘要】 广义周期系统的研究是近年来人们特别关注的问题之一,它的核心问题主要有两个,一是通过受限等价变换将系统分解为两个子系统,分别来研究系统的性能;二是通过求解广义Lyapunov不等式来研究系统的允许性等问题。随着广义周期系统应用领域的不断扩大,对广义周期系统的理论研究也在不断深入。本文研究了广义周期系统的稳定性及相关控制问题,结合正常周期系统理论、鲁棒控制理论,H_∞控制理论,采用Lyapunov方法,单值矩阵法,LMI技术等深入地研究了广义周期系统的稳定性及相关控制问题。主要工作有以下几个方面: (1)针对广义连续周期系统,建立了广义Lyapunov不等式,并利用不等式给出了系统允许的充要条件,在此基础上讨论了系统二次允许的充分必要条件,同时给出控制器的设计方法,这对于进一步研究广义周期系统打下了坚实的基础。 (2)针对广义不确定周期系统,研究了系统的鲁棒稳定性,给出了充要条件和一族状态反馈鲁棒镇定器的设计方法,并讨论了二次稳定性与鲁棒稳定性的关系。 (3)针对广义连续周期系统,讨论了系统在两种特殊情况下基于状态反馈的H_∞控控制问题的解,在较为一般的假设下,证明了它和一个正常周期系统的状态反馈H_∞控制问题的等价性,并利用微分Riccati不等式,给出问题有解的充分必要条件及状态反馈控制器的一族解。 (4)针对广义连续周期系统,研究了系统的脉冲能控性,利用系统的原系数和可计算的矩阵描述了系统脉冲能控的直接特征,并利用算子表达式和Gramian矩阵给出了上述问题简明的判别准则。更多还原

【Abstract】 In recent years, the research on periodic descriptor systems is one of the most concerned questions. There are two important central problems. First, the system can be divided into two subsystems by using a restricted equivalent transformation, then study and analyze the performance of the system respectively;Second, the admissibility of the system and other related problems can be studied by solving the generalized Lyapunov inequality. With the enlargement of the singular systems application, the study on periodic descriptor systems theory is being probed further progressively. We discussed the stability and related control problems for periodic descriptor systems. Combing the standard periodical system theory with robustness control theory and H_∞ control theory, using Lyapunov method, monodromy matrices and LMI, this thesis has given a further investigation about the stability analysis and control problems of the above systems. The main contributions are as follows:(1) For the periodic continuous singular systems, the necessary and sufficient condition was presented for impulse-free and asymptotic stability of 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 periodical systems.(2) For linear uncertain 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 linear periodic continuous descriptor systems, he state feedback H_∞ control problem in two special cases were discussed. Under two common assumptions, the equivalenceof this problem and the feedback Hx control problem for standard state-space linear periodicalsystems was derived. By means of differential Riccati inequality, the necessary and sufficient condition for this problem and the existence of a kind of controller were given.(4) For continuous singular periodic systems, the problem of impulsive controllability was discussed. The direct characterizations of the above problem were given directly in terms of the original system coefficients and their derivatives, and the explicit criterions were presented by using operator expression and the rank of Gramian matrices.更多还原