【作者】 杨露；

【导师】 任英；

【作者基本信息】 大连海事大学 ， 运筹学与控制论， 2010， 硕士

【摘要】 在实际的工程应用问题中,由于存在着诸如由参数的测量误差、运行环境的变化等所导致的不确定性,使得我们很难得到被控系统对象的精确模型。研究奇异系统的鲁棒控制,就是研究当系统模型存在不确定性时,如何设计控制器,使得对于满足一定范围的参数不确定性,闭环系统仍能保持稳定,并使之保持一定的动态性能。而奇异系统由于比正则系统具有更广泛的形式,其研究因此也有着更为重要的理论意义和实际意义。本论文主要研究了线性奇异时滞系统的鲁棒控制问题,以Lyapunov泛函和线性矩阵不等式为主要工具,分别对不确定连续时间奇异时滞系统和不确定离散时间奇异系统的鲁棒稳定性进行了分析。主要内容包括以下两个方面：1.针对具有时变时滞的连续时间标称奇异系统,通过选取恰当的Lyapunov泛函给出了更简便的具有LMI线性矩阵不等式形式的鲁棒稳定的充分条件,并将结论推广到不确定情形中去。值得注意的是该条件对时滞d(t)是没有任何限制要求的。同时,给出具体算例来验证结论的有效性。2.针对具有时变时滞的不确定离散时间奇异系统,首先给出了当时滞有界时标称系统鲁棒稳定的线性矩阵不等式条件,并将结论推广到不确定的情形中去。同时,给出具体算例来验证结论的有效性。更多还原

【Abstract】 It makes us impossible to get the precise model of controlled objects in most practical engineering applications, due to the existence of uncertainties caused by the measurement parameter-error, the changing of running condition, etc. To study on robust control for singular systems, is to research how to design a control law to stabilize the resultant closed-loop system and keep some dynamic performances when satisfied a range of parameter uncertainties. Therefore, the study on singular systems is significant both in theory and in practice, because singular systems have more widespread form compared with regular ones.The robust control for linear singular systems with time-delay is studied on the basis of Lyapunov function and linear matrix inequality(LMI) in this dissertation, including the robust stability of uncertain continuous-time singular systems and uncertain discrete-time singular systems with time delays. The main contents of this dissertation are outlined as follows.1. A sufficient condition of robust stability with LMI form is presented according to nominal continuous-time singular systems with time-varying delays, by selecting the proper Lyapunov function, and the condition is delay-independent. Then the conclusion is extended to the uncertain case. It is worth nothing that the condition has no limitation requirements on the time-delay d(t), and numerical examples show the effectiveness of the conclusion.2. A new sufficient condition of robust stability with LMI form is presented at first according to nominal discrete-time singular systems with time-varying delays when the varying time-delay is bounded. Then the conclusion is extended to the case of uncertain condition, and numerical examples show the effectiveness.更多还原