模糊控制器设计外文资料翻译--离散模糊双线性系统的静态输出反馈控制(编辑修改稿)

模糊控制器设计外文资料翻译--离散模糊双线性系统的静态输出反馈控制(编辑修改稿)内容摘要：

umerical examples In this section, an example is used for illustration. The considered DFBS is 1: ( 1 ) ( ) ( ) ( ) ( )( ) ( ) 1 , 2iii i iiR if y is Mthe n x t A x t B u t N x t u ty t C x t i    Where 1 2 1 2 1 29 . 7 8 1 0 1 0 1 0 1, , ,5 1 0 5 1 0 0 1 1A A N N B B                                   121 0 , 1 0 .CC   The membership functions are defined as 1 11( ) (1 c os( ) ) / 2 ,M yy  2111( ) 1 ( )MMyy . By letting 11 12 21 2 , , 1,         applying Theorem 2 and solving the corresponding LMIs, we can obtain the following solutions:   12 1 . 5 0 1 4 ,1 1 . 0 7 9 0 2 . 2 7 8 5 , 3 . 0 4 5 2 .2 . 2 7 8 5 0 . 5 9 8 4 FQ F    Simulation results with the initial conditions:   respective, are shown in and . One can find that all these state converge to the equilibrium state after 17 seconds. 0 2 4 6 8 10 12 14 16 18 202 1 . 51 0 . 500 . 511 . 5tx(t)x1x2 0 2 4 6 8 10 12 14 16 18 20 0 . 6 0 . 4 0 . 200 . 20 . 40 . 60 . 8tu(t) . State responses of system . Control trajectory of system 5 Conclusions In this paper, a new and simple approach for designing a fuzzy static output feedback controller for the discretetime fuzzy bilinear system is presented. The result is formulated in terms of a set of LMIbased conditions. By the proposed approach, the local output matrices are not necessary to be the same. Thus, the constraints had been relaxed and applicability of the static output feedback is increased. References [1] Wang R J, Lin W W and Wang W J. Stabilizability of linear quadratic state feedback for uncertain fuzzy timedelay systems [J]. IEEE Trans. Syst., Man, and Cybe., 2020, 34(2):12881292. [2] Cao Y Y and Frank P M. Analysis and synthesis of nonlinear timedelay systems via fuzzy control approach [J]. IEEE Trans. Fuzzy Syst., 2020, 18(2): 200211. [3] Yoneyama J. Robust stability and stabilization for uncertain TakagiSugeno fuzzy timedelay systems [J]. Fuzzy Sets and Syst., 2020, 158(4): 115134. [4] Shi X Y and Gao Z W. Stability analysis for fuzzy descriptor systems [J]. Systems Engineering and Electronics, 2020, 27(6):10871089. (In Chinese) [5] Jiang X F and Han Q L. On designing fuzzy controllers for a class of nonlinear worked control systems[J]. IEEE Trans. Fuzzy Syst., 2020, 16(4): 10501060. [6] Lin C, Wang Q G, Lee T H, et al. Design of observerbased H∞ control for fuzzy timedelay systems[J]. IEEE Trans. Fuzzy Syst., 2020, 16(2): 534543. [7] Kim S H and Park P G. Observerbased relaxed H∞ control for fuzzy systems using a multiple Lyapunov function[J]. IEEE Trans. Fuzzy Syst., 2020, 17(2): 476484. [8] Zhang Y S, Xu S Y and Zhang B Y. Robust output feedback stabilization for uncertain discretetime fuzzy markovian jump systems with timevarying delays[J]. IEEE Trans. Fuzzy Syst., 2020, 17(2): 411420. [9] Chang Y C, Chen S S, Su S F, et al. Static output feedback stabilization for nonlinear interval timedelay systems via fuzzy control approach [J]. Fuzzy Sets and Syst., 2020, 148(3): 395410. [10] Chen S S, Chang Y C, Su S F, et al. Robust static outputfeedback stabilization for nonlinear discretetime systems with time delay via fuzzy control approach[J]. IEEE Trans. Fuzzy Syst., 2020, 13(2): 263272. [11] Huang D and Nguang S K. Robust H∞ static output feedback control of fuzzy systems: a LMIs approach [J]. IEEE Trans. Syst., Man, and Cybe., 2020, 36: 216222. [12] Mohler R R. Nonlinear systems: Application to Bilinear control [M]. Englewood Cliffs, NJ: PrenticeHall, 1991 [13] Dong M and Gao Z W. H∞ faulttolerant control for singular bilinear systems related to output feedback[J]. Systems Engineering and Electronics, 2020, 28(12):18661869. (In Chinese) [14] Li T H S and Tsai S H. TS fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems [J]. IEEE Trans. Fuzzy Syst., 2020, 3(15):494505. [15] Tsai S H and Li T H S. Robust fuzzy control of a class of fuzzy bilinear systems with timedelay [J]. Chaos, Solitons and Fractals (2020), doi: . [16] Li T H S, Tsai S H, et al, Robust H∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems [J]. IEEE Trans. Syst., Man, and Cybe., 2020, 38(2) : 510526. 离散模糊双线性系统的静态输出反馈控制 摘要 ：研究了一类离散模糊双线性系统 (DFBS)的静态输出反馈控制问题。 使用并行分布补偿算法(PDC)，得到了闭环系 统渐近稳定的充分条件，并把这些条件转换成线性矩阵不等式 (LMI)的形式，使得模糊控制器可以由一组线性矩阵不等式的解得到。 和现有的文献相比，这种方法不要求相同的输出矩阵和相似转换等条件。 最后，通过仿真例子验证了方法的有效性。 关键词 ：离散模糊双线性系统；静态输出反馈控制；模糊控制；线性矩阵不等式； 0 引言 众所周知，基于 TS 模型的模糊控制是研究非线性系统比较成功的方法之一，在稳定性分析和控制器设计方面，已有很多成果面世 [1][10]。 然而大部分控制器是关于状态反馈或基于观测器的状态反馈 [1][3]，关 于输出反馈的结果则很少 [4][10]。 输出反馈控制直接利用系统的输出量来设计控制器，不用考虑系统状态是否可测可观，而且静态输出反馈控制器结构简单，因此具有良好的应用价值。 文 [5][6]研究了模糊时滞系统的静态输出反馈控制问题，文 [8]第一次提出了模糊静态输出反馈 H∞ 控制的问题。 但是上述结果所得到的条件常常是双线性矩阵不等式 (。