【作者】 张娜；

【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】 时滞广义系统是一类更为广泛的滞后系统，在工程系统、制造系统、人口生态系统、经济系统、电路网络系统和社会系统等系统中都有重要的应用。时滞是影响广义系统性能的重要因素，以H_∞范数描述的H_∞控制能够使系统具有优良的性能，因此关于时滞广义系统的H_∞控制的研究有重要的理论意义和实用价值。论文通过构造适当的Lyapunov-Krasovskii泛函，应用积分不等式、矩阵奇异值理论和线性矩阵不等式(LMI)等方法，研究了时滞广义系统H_∞控制问题。论文的主要内容如下：首先，将机械系统模型转化成状态方程形式，利用广义系统理论研究机械系统的时滞相关H_∞控制问题，给出机械系统正则、无脉冲、渐近稳定且具有给定的H_∞抑制扰动的条件。其次，研究时滞广义系统的记忆反馈非脆弱H_∞控制问题。通过构造适当的Lyapunov-Krasovskii泛函、利用Schur补引理和新的积分不等式，给出了闭环系统正则、无脉冲、渐近稳定且具有给定的H_∞抑制扰动的时滞相关条件。然后，研究具有饱和因子的不确定时滞广义系统的时滞相关鲁棒H_∞控制问题，利用Lyapunov-Krasovskii泛函理论，用线性矩阵不等式方法和矩阵奇异值理论，给出了鲁棒H_∞控制器的设计方法。最后，研究具有饱和因子的多时滞广义系统的时滞相关保成本H_∞控制，利用线性矩阵不等式方法并结合矩阵奇异值理论，给出了鲁棒H_∞保成本控制器存在的充分条件以及相应控制器的设计方法。更多还原

【Abstract】 The singular system with time-delay is a class of time-delay systems broader thanothers. Singular systems have found in many practical applications, such as inengineering systems, manufacturing systems, population ecology systems, economicsystems, circuit network system, social systems and so on. Time delays are importantfactors which affect the performance of singular systems. The H_∞control by H_∞norm to describe can make the system has excellent performance. Therefore, theresearch for singular systems with time-delays has important theoretical and practicalsignificance.This dissertation studies the problem of H_∞control for singular systems withtime-delays by constructing appropriate Lyapunov-Krasovskii function, combiningwith integral inequality, singular value theory and linear matrix inequality (LMI)approach. The main works are as follows:Firstly, the mechanical system model is transformed into state equation. Theproblem of delay-dependent H_∞control for mechanical system is investigated by thesingular system theory. A sufficient condition is given to guarantees the mechanicalsystem is regular, impulse free, stable and satisfies the H_∞performance.Secondly, the problem of memory feedback non-fragile H_∞control for singularsystems with state-delay is dealt with. By constructing appropriate generalizedLyapunov-Krasovskii function, using Schur-complement Lemma and a new integralinequality, then a sufficient condition is given to guarantees the resultant closed-loopsystem is regular, impulse free, and stable with a H_∞norm bound constraint.Thirdly, the problem of delay-dependent robust H_∞control for time-delaysingular systems with saturating actuators and parameter uncertainties is investigated.Based on Lyapunov-Krasovskii stability theory, the design method of controller isgiven by the LMI method and the singular value theory.Finally, the problem of robust guaranteed cost H_∞control problem for a class ofsingular systems with multiple time delays subject to input saturation. Based on LMIapproach and the singular value theory, sufficient conditions for the existence of guaranteed cost H_∞control law and corresponding guaranteed cost performanceindex are obtained.更多还原