【作者】 程东东；

【导师】 马跃超；

【作者基本信息】 燕山大学 ， 运筹学与控制论， 2012， 硕士

【摘要】 鲁棒控制理论结合系统模型参数的不确定性和外部扰动的不确定性，研究系统的鲁棒性能，弥补了现代控制理论的需要对象是精确数学模型的缺陷，使得系统的分析和综合方法更加有效、实用。近年来，鲁棒耗散滤波器引起越来越多的关注，在实际工业中，经常遇到参数不确定和含有时滞的耗散滤波器设计问题，因此，研究耗散滤波问题具有重要的理论意义和应用价值。论文研究了时滞广义系统的鲁棒耗散滤波器的设计问题，文中所研究的系统模型和设计方法是已有相关文献模型和原有方法的推广和改进。主要内容如下：首先，简要的介绍了鲁棒控制的产生和应用背景、鲁棒耗散滤波理论的发展、研究概况及鲁棒耗散滤波的研究方法。其次，研究了一类不确定时滞广义系统的鲁棒耗散滤波器设计问题，参数不确定性具有线性分式形式。基于Lyapunov稳定理论，通过选取适当的Lyapunov函数，分别给出了系统的鲁棒耗散滤波存在的充分条件和设计方法。仅通过求解相应的线性矩阵不等式(linear matrix inequality, LMI)就可得到鲁棒耗散滤波器。接着，针对一类参数不确定的时滞T-S模糊广义系统，研究了该系统的鲁棒耗散滤波器设计，给出了其鲁棒耗散滤波器存在的充分条件。然后，针对一类带有非线性扰动的时滞广义系统，通过构造Lyapunov函数和运用线性矩阵不等式的方法，研究其鲁棒耗散滤波，数值算例验证了所给算法的有效性。最后，针对一类具有马尔可夫跳变参数的不确定随机广义时滞系统，讨论了该类系统的鲁棒非脆弱耗散滤波问题，运用线性矩阵不等式给出了系统的非脆弱滤波器存在的可解性条件。通过数值算例表明了该方法的有效性。更多还原

【Abstract】 Robust control theory combining with parameter uncertainties and uncertainty ofexternal disturbance, researches the robust performance of system. It makes up for the lackof modern control theory needing to mathematical models, and makes the method ofsystem analysis and synthesis more effective and practical. In recent years, the robustdissipative filter is caused more and more attention. In actual industry, people often designthe dissipative filters with time-delay and parameter uncertainties. Therefore, dissipativefiltering problems have important significance and value.In this dissertation, the robust dissipative filter design method for singular systems isconsidered. The system’s models and design methods are more generalized than othersexisting literatures. The main content as follows:First of all, the generation and application background of robust control areconsidered. The robust dissipative filtering theory, the recent development and theresearch method for the robust dissipative filtering are also introduced.Secondly, the robust dissipative filtering of singular systems with time-delay andparameter uncertainties are separately investigated. The uncertainties are in a fractionalform. Based on the Lyapunov theory, with constructing a Lyapunov function, the existingconditions and design method of dissipative filtering problem is solved, and the desiredproblem of filter can be constructed by solving the corresponding linear matrix inequality.Thirdly, the problem of robust dissipative filtering for a class of time-varyingtime-delay T-S fuzzy singer systems with parameter uncertainties is considered. Thesufficient conditions on the existence of robust dissipative filters are derived.Fourthly, by structuring Lyapunov functions, the robust dissipative filter for a class oftime-delay singular systems with nonlinear perturbation and parameter uncertainties canbe obtained by solving the corresponding linear matrix inequality. Numerical examplesare provided to illustrate the effectiveness of the design approach.At last, the problem of robust and non-fragile dissipative filter is investigated for aclass of uncertain stochastic time-delay singer systems with Markovian jump parameters.A sufficient condition for the existence of non-fragile filter is derived in the form of linearmatrix inequality(LMI). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.更多还原