【作者】 巩诚；

【导师】 苏宝库；

【作者基本信息】 哈尔滨工业大学 ， 控制科学与控制， 2008， 博士

【摘要】 非线性和时滞是工程领域中普遍存在的现象,也是控制理论研究的热点和难点之一。Takagi-Sugeno（T-S）模糊模型将专家经验与传统的控制理论相结合,己逐渐成为研究复杂非线性系统的重要方法,受到了众多学者注意。因此,对T-S模糊时滞系统的研究,不仅具有重要的理论意义,也具有非常重要的实际意义。本文基于Lyapunov函数方法,并结合线性矩阵不等式（LMI）技术,对不确定T-S模糊时滞系统和不确定随机T-S模糊时滞系统的稳定性、H_∞控制、H_∞滤波、L₂-L_∞滤波等问题进行了研究,其主要工作和研究成果体现如下:1.研究了不确定连续（和离散）T-S模糊时滞系统稳定性问题,并在此基础上研究了不确定连续（和离散）T-S模糊时滞系统的H_∞控制问题。本文在前人研究的基础上,构造了一个新的Basis-dependent Lyapunov- Krasovskii函数,在此基础上以LMI的形式给出了一个保证不确定T-S模糊时滞系统渐进稳定同时具有H_∞性能的时滞依赖状态反馈控制器的设计方法,该控制器的设计方法与现有文献相比,具有较低的保守性。同时,我们将此Basis-dependent Lyapunov-Krasovskii函数方法应用到离散不确定T-S模糊时滞系统,并得到了相应的离散系统的时滞依赖鲁棒H_∞控制器的设计方法。2.研究了不确定连续T-S模糊时滞系统的H_∞滤波和L₂-L_∞滤波问题。在研究了不确定连续T-S模糊时滞系统的时滞依赖H_∞控制的基础上,给出了一个保证滤波误差系统在参数不确定条件下具有事先指定的鲁棒H_∞干扰抑制水平γ的LMI条件和一个相应的L₂-L_∞抑制条件。并以LMI的形式给出了一个具有较低保守性的不确定T-S模糊时滞系统的时滞依赖鲁棒H_∞滤波器的设计方法和L₂-L_∞滤波器的设计方法。3.研究了不确定随机T-S模糊时滞系统的鲁棒H_∞控制问题。首先,基于一个新的Basis-dependent Lyapunov-Krasovskii函数,我们以LMI的形式给出了保证不确定随机T-S模糊系统均方渐进稳定,且具有均方意义上的H_∞性能的充分条件,然后基于此充分条件,以LMI的形式给出了一个具有较低保守性的不确定随机T-S模糊时滞系统的时滞依赖鲁棒H_∞控制器的设计方法。4.研究了不确定随机T-S模糊时滞系统的H_∞滤波和L₂-L_∞滤波问题。在研究了不确定随机T-S模糊时滞系统均方H_∞控制的基础上,我们首先以LMI的形式给出了保证滤波误差系统具有均方意义上的H_∞性能的一个充分条件,然后在此基础上我们给出了一个不确定随机T-S模糊时滞系统的鲁棒H_∞滤波器的设计方法,其鲁棒L₂-L_∞滤波器设计方法也以相似的推导方法给出。5.最后,我们应用本文所提出的T-S模糊时滞系统的控制方法,研究了具有能量有界干扰下的卡车拖车倒车问题。本文首先为卡车拖车系统建立了具有能量有界干扰和状态时滞的不确定T-S模糊时滞系统模型,然后以LMI的形式给出了保证倒车系统渐进稳定,同时具有H_∞性能的时滞依赖鲁棒状态反馈控制器。仿真结果验证了所提方案的可行性。更多还原

【Abstract】 Nonlinearity and time delay can be found in various engineering systems, which are hotspots and difficulties in area of control. Takagi-Sugeno （T-S） model combining the traditional control theories with expert knowledge has become the important method of dealing with complex nonlinear systems and received more and more attention. So, it is of great theoretical and practical significance that research on the T-S fuzzy time-delay systems.Based on Lyapunov functional method, by using linear matrix inequality （LMI）, this dissertation studies the problems of delay-dependent H_∞control, H_∞filtering, L₂-L_∞filtering for uncertain T-S fuzzy time-varying delay system and uncertain stochastic T-S fuzzy time-varying delay system. The main work and contribution of this dissertation are listed as follows.1. The delay-dependent robust stability problem of uncertain continue （discrete） T-S fuzzy time-varying delay system is studied, based on this study, we researched the H_∞problem for the uncertain continue （discrete） T-S fuzzy time-varying delay systems.Based on the former research, we propose a new Basis-dependent Lyapunov-Krasovskii functional. Then, we present a delay-dependent state feed- back robust H_∞controller in term of LMIs, this controller guarantees the continue uncertain T-S fuzzy time-varying delay system not only asymptotically stable but also a prescribed H_∞attenuation level. Compared with the current literatures, this controller is much less conservative. At the same time, we extend this Lyapunov-Krasovskii functional method to discrete uncertain T-S fuzzy time-varying delay system, and also obtain a design scheme of delay-dependent robust H_∞controller with less conservatism in term of LMIs2. Delay-dependent robust H_∞filtering and L₂-L_∞filtering problems of uncertain continue T-S fuzzy time-varying delay systems are studied.Based on the results of H_∞control for uncertain continue T-S fuzzy time- varying delay system, we propose a delay-dependent criterion in term of LMIs, which guarantees a prescribed H_∞attenuation levelγfor the filtering error system. Then, a delay-dependent robust H_∞filter with less conservatism is proposed in LMIs. The corresponding robust L₂-L_∞filter is given by using the same method.3. Delay-dependent robust H_∞control problem of uncertain stochastic continue T-S fuzzy time-varying delay system is studied.First, based on the new Basis-dependent Lyapunov-Krasovskii functional, we propose a sufficient criterion in term of LMIs such that the closed-loop uncertain stochastic continue T-S fuzzy time-varying delay system is asymptotically stable in mean square and a prescribed H_∞performance in mean square is achieved. Then based on this sufficient condition, the robust H_∞controller with less conservatism is presented in term of LMIs.4. Delay-dependent robust H_∞filtering and L₂-L_∞filtering problems of uncertain stochastic continue T-S fuzzy time-varying delay systems are studied.Based on the results of H_∞control for uncertain stochastic continue T-S fuzzy time-varying delay system, we propose a delay-dependent criterion in term of LMIs, which guarantees a prescribed H_∞attenuation levelγin mean square for the filtering error system. Then, a delay-dependent robust H_∞filter is proposed in LMIs. The corresponding robust L₂-L_∞filter is given by using the same method.5. Finally, applying the results of uncertain continue T-S fuzzy time-varying delay system proposed in this dissertation, we study the backing-up control of truck-trailer with bounded energy disturbance.We model a uncertain continue T-S fuzzy time-varying delay model for the truck-trailer system with energy-bounded disturbance and state delay, then, we propose a robust H_∞controller in term of LMIs, which guarantees the truck-trailer system a prescribed H_∞performance. Simulation demonstrates the effectiveness of the fuzzy controller design scheme we proposed.更多还原