【作者】 李华；

【导师】 赵军；

【作者基本信息】 东北大学 ， 控制理论与控制工程， 2012， 硕士

【摘要】 切换模糊系统是指子系统是模糊系统的一类切换系统,它的研究以切换系统理论和模糊系统理论为基础,有着广泛的理论意义和实际应用价值。在实际工程中,很多因素都能引起不确定性和时滞,这种不确定性和时滞可能会导致系统不稳定；另一方面,传统的鲁棒控制器具有一定的脆弱性,可能造成闭环系统性能指标下降甚至不稳定。因此,研究带有结构不确定性及时滞的切换模糊系统的鲁棒镇定问题和非脆弱保成本控制问题具有重要的理论和实际意义。本文通过两种不同的方法对一类带有结构不确定性及时滞的切换模糊系统进行研究,主要工作概述如下：首先,研究了一类带有结构不确定性及时滞的切换模糊系统的鲁棒镇定问题。利用凸组合方法设计切换律,并通过设计状态反馈控制器使得此类切换模糊系统渐近稳定。由于在设计过程中,寻找可行的凸组合往往是一个NP难问题,因此,我们给出了一种寻找可行凸组合的算法。通过数值例子验证了所提方法的有效性。其次,研究了一类带有结构不确定性及时滞的切换模糊系统的非脆弱保成本控制问题。利用多Lyapunov函数方法设计切换律,并通过设计非脆弱保成本控制器使得此类切换模糊系统渐近稳定,并且保证成本函数不大于某一上界。由于不同的可行解会导致不同的成本上界,因此,我们给出了寻找成本函数最优值的方法。通过例子验证了所提方法的有效性。最后,对本文的主要结果进行了总结,此外,我们还讨论了切换模糊系统的一些值得今后深入研究的问题以及本文所提方法的不足之处。更多还原

【Abstract】 Switched fuzzy systems refer to a class of switched systems whose subsystems are fuzzy systems. The study of switched fuzzy systems is based on switched systems theory and fuzzy systems theory, and has theoretical importance and extensive application value. In practical engineering, many factors can cause uncertainty and time-delay which may lead to instability. On the other hand, the traditional robust controllers have some certain vulnerabilities, which may also bring about the bad performance indexes, even the instability of the closed-loop system. Therefore, to study the robust stabilization problem and the non-fragile guaranteed cost problem for switched fuzzy systems with structural uncertainties and time-delay has theoretical and practical significance.In this thesis, we investigate a class of switched fuzzy systems with structural uncertainties and time-delay by employing two different methods. The main results are as follows:Firstly, the robust stabilization for a class of switched fuzzy systems with structural uncertainties and time-delay is studied. The switching law is designed via the convex combination technique, meanwhile, state feedback controllers are designed to make the switched fuzzy system asymptotically stable. Because looking for a set of feasible convex combinations is usually a NP-hard problem in the design process, we present an algorithm to find the feasible convex combinations. The effectiveness of the proposed method is demonstrated by a numerical example.Secondly, the problem of the non-fragile guaranteed cost control for a class of switched fuzzy systems with structural uncertainties and time-delay is addressed. The switching law is designed by the multiple Lyapunov functions technique, moreover, the non-fragile guaranteed cost controllers are designed not only to make the closed-loop switched fuzzy systems asymptotically stable, but also to guarantee the cost function no more than a certain upper bound. Since the different feasible solutions can result in the different cost upper bounds, we present a method to search for the optimal value of the cost function. An example is given to illustrate the effectiveness of the proposed method.Finally, the main results of the thesis are summarized. In addition, some open problems of the switched fuzzy systems and the shortcomings of the proposed methods are also discussed which deserve further study.更多还原