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摘要: 研究基于T-S (Takagi-Sugeno)模糊模型的采样控制系统鲁棒耗散控制问题. 利用2阶B-L (Bessel-Legendre)不等式和整个采样间隔
$\left[ {{t_k},{t_{k + 1}}} \right)$ 的特征信息, 提出一个基于B-L不等式的双边时间相关不连续L-K (Lyapunov-Krasovskii)泛函. 使用提出的L-K泛函和改进的自由矩阵不等式, 建立了确保系统严格($\mathcal{Q}$ ,$\mathcal{S}$ ,$\mathcal{R}$ )-$\gamma$ -耗散的充分条件. 基于所得耗散条件, 给出了T-S模糊采样控制器的设计方法, 并用于处理卡车拖车的控制问题. 仿真结果表明所提出的控制器设计方法非常有效.-
关键词:
- T-S模糊模型 /
- 采样控制系统 /
- 基于B-L不等式的双边时间相关不连续L-K泛函 /
- T-S模糊采样控制器
Abstract: This paper investigates the problem of robust dissipative control for sampled-data control system based on Takagi-Sugeno (T-S) fuzzy model. By employing the second-order Bessel-Legendre (B-L) inequality and the characteristic information on the whole sampling interval$\left[ {{t_k},{t_{k + 1}}} \right)$ , a B-L-inequality-based two-side time-dependent discontinuous Lyapunov-Krasovskii (L-K) functional is proposed. By using the proposed functional and improved free-matrix-based inequality, a sufficient condition is established to ensure that the sampled-data system is strictly ($\mathcal{Q}$ ,$\mathcal{S}$ ,$\mathcal{R}$ )-$\gamma$ -dissipative. Based on the obtained condition, a method to design desired T-S fuzzy sampled-data controller is presented, which is applied to deal with the control problem of a truck-trailer system. The obtained results show that the proposed design approach for the controller is very effective. -
表 1 对不同
$ h_2 $ 的$\gamma_{\max}$ Table 1
$\gamma_{\max}$ for different$ h_2 $ $h_2$ 0.05 0.10 0.15 0.20 0.25 0.35 文献 [30] 0.9971 0.9671 0.9311 0.8842 0.8193 − 推论 1 1.0636 1.0463 1.0264 0.9978 0.9554 0.7484 定理 2 1.0643 1.0472 1.0272 0.9994 0.9559 0.7564 表 2 对不同
$ h_1 $ 的$\gamma_{\max}$ Table 2
$\gamma_{\max}$ for different$ h_1 $ $h_1$ 0.10 0.15 0.20 0.25 0.3 0.35 定理 2 0.8108 0.8350 0.8546 0.8716 0.8854 0.9026 表 3 对不同
$ h_1 = h_2 $ 的$\gamma_{\max}$ Table 3
$\gamma_{\max}$ for different$ h_1 = h_2 $ $h_1=h_2$ 0.05 0.10 0.15 0.20 0.25 0.35 定理 2 1.0679 1.0572 1.0447 1.0283 1.0072 0.9026 -
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