【作者】 周朝霞；

【导师】 张肃宇；

【作者基本信息】 南昌大学 ， 控制理论与控制工程， 2007， 硕士

【摘要】 众所周知非线性系统广泛存在于客观世界，时滞为一般系统所固有，而不确定性在所难免，因此对不确定时滞非线性系统的鲁棒稳定性进行研究显得特别重要。故不确定时滞非线性系统的鲁棒稳定性研究是当前控制界研究的热点和难点之一。本文归纳了现有一些文献所提出的鲁棒稳定性定理，并在此基础上对时滞非线性系统的鲁棒稳定性分析及控制方面做了一些工作。首先，在Lyapunov稳定性理论基础上，针对T-S动态模糊模型，归纳了利用线性矩阵不等式和并行分布补偿原理(PDC)及模糊模型相除补偿方法(CDF)分析模糊系统所得到的稳定性定理和保证系统稳定的模糊控制器设计，对上述方法做了一个比较分析和概括总结；基于T-S动态模糊模型，归纳了不确定连续模糊和离散模糊非线性系统的鲁捧稳定性定理。其次，对具有时滞的非线性系统，利用模糊T-S模型对其进行模糊建模，采用分段Lyapunov函数方法和不等式处理技巧，得到系统鲁棒稳定的充分条件，并在此基础上提出了模糊控制器的设计方法，使得整个系统是鲁棒稳定的。最后，介绍了一类同时存在两种不确定性的非线性时滞系统鲁棒稳定性条件及保证系统鲁棒稳定的模糊控制器设计方法，对该鲁棒稳定性条件的证明做了很详细的推导运算。更多还原

【Abstract】 As we all know that nonlinear systems exist in the world extensively, time delays are inherent in systems and uncertainties are not avoidable. So it is important to investigate the robust stability analysis of uncertain nonlinear systems with time delays. Now it is one of the hotspots and also the difficulties in control domain. This paper summarizes some of theories of robust stability and based on the existing this, some work has been done in this paper on robust stability analysis and control of time-delay nonlinear systems.Firstly, On the basis of Lyapunov stability theories, The theorems of stability using the approach of linear matrix inequality and the principle of PDC and the concept of CDF (compensation and division for fuzzy model) are summarized in this paper and a kind of fuzzy controller which makes whole systems gradual stabilizing is got based on the T-S fuzzy dynamic model. I compare the above-mentioned methods and draw a conclusion after carefully analyzing. And the theorems of robust stability for uncertain continuous and discrete fuzzy nonlinear systems are summarized based on the T-S fuzzy dynamic model.Secondly, The fuzzy T-S model is used to approximate to time-delay nonlinear systems. And the sufficient condition of robust stability for time-delay nonlinear systems is put forward based on piecewise Lyapunov function and inequality method. In addition, a kind of fuzzy controller which makes whole systems stabilizing is designed in the paper.At last, the robust stability condition of time-delay nonlinear systems with two kinds of uncertain is summarized and a kind of fuzzy controller that makes the whole systems robust stability is introduced. At the same time, detailed illation of proof for this robust stability condition is put forward in the paper.更多还原