【作者】 刘勇；

【导师】 罗跃生；

【作者基本信息】 哈尔滨工程大学 ， 系统理论， 2009， 硕士

【摘要】 对于一个系统而言,稳定是被关注的首要问题.在工程实践中,时滞是普遍存在的.众所周知,时滞的存在会对系统的稳定性产生很大的影响,这是因为时滞的存在将会改变系统的特征方程,所以时滞成为系统不稳定的重要因素.因此对时滞系统加以专门的研究是非常重要的.本文首先主要研究了依赖型的线性不确定时滞系统的渐进稳定性和鲁棒H∞控制器的设计问题.基于线性矩阵不等式和Lyapunov稳定性理论,通过构造合适的Lyapunov函数,讨论了具有一定的匹配条件及数值界的参数不确定性的时滞系统.利用积分不等式引入自由权矩阵的方法,提出了此类系统渐近稳定的充分条件及最大时滞,我们得到的结果具有较小的保守性和较少的矩阵变量；我们又给出了时滞不确定系统保持渐进稳定的控制器设计方法.本文并对该方法进行了验证,结果表明设计方法是有效的.然后,对于系统的状态是不可测量时,我们讨论了依赖型的时滞不确定系统的无偏滤波器设计方法,给出了系统鲁棒渐近稳定的充分条件和独立型的时滞不确定系统的无偏滤波器设计相比较具有较小的保守性；又讨论了时滞不确定系统的常规滤波器设计问题,并比较了两种滤波器设计的优缺点.最后,当系统是非线性的情况下,基于T-S模型,通过引入自由权矩阵的方法,我们研究了一类模糊不确定时滞系统的鲁棒渐进稳定性及状态反馈H∞模糊控制器设计的问题,给出了用线性矩阵不等式表示的状态反馈H∞模糊控制器存在的充分条件.更多还原

【Abstract】 Stability is of primary impotance for a system, and time-delay can be found in the engineering practices. As we all know, the existence of time delay can be bring in a large number of exffects to the stability of the systems, because the existence of time delay will alter the characteristic equation of the systems, and time delay becomes the main factor to cause instability of the system. Therefore, the specialized research of time-delay is very important.Firstly, this paper discussed principally the asympototic stability and robust H∞controller of problems of the dependent of linear uncertain tine-delay systems. Based on linear matrix inequality method and Lyapunov stability theory, and by constructing the appropriate Lyapunov function, we have studied the time-delay systems which possess definite matching conditions and valued-bounded uncertainty. Introducting some free weighting matrixes by using the integral inequality, we gived the sufficient conditions of the systems and the largest tine delay. The results we have obtained have less conservative and matrix variables. In this paper we also gived the design approach of controller keeping the uncertain time-delay systems asympototical stabilization. This method is proved, and the results show the effectiveness of the proposed method.Seconedly, when the state is not measurable, we discussed the design approach of unbiased filter of linear uncertain tine-delay systems, giving the sufficient conditions of robust asympototic stability of the systems, comparing with the independent time-delay uncertain system, and our results of the unbiased filter design have less conservative. Meanwhile, we also discuss the problems of conventional filter of linear uncertain tine-delay systems, and compare advantages and disadvantages with the unbiased filter design. Lastly, considering the nonlinear system, introducting some free matrixes by Newton-leibniz formula and based on T-S model, we discussed the problem of robust asympototic stability and state feedback H∞fuzzy controller design of a class of fuzzy uncertain time-delay systems, giving the sufficient conditions of state feedback H∞fuzzy controller in terms of a strict linear matrix inequality.更多还原