College of Information Science and Engineering, Northeastern University, Shenyang 110004, PR China.
ISA Trans. 2012 Nov;51(6):771-7. doi: 10.1016/j.isatra.2012.06.014. Epub 2012 Jul 21.
This paper studies the problem of state feedback controller design for a class of nonlinear systems, which are described by continuous-time affine fuzzy models. A convex piecewise affine controller design method is proposed based on a new dilated linear matrix inequality (LMI) characterization, where the system matrix is separated from Lyapunov matrix such that the controller parametrization is independent of the Lyapunov matrix. In contrast to the existing work, the derived stabilizability condition leads to less conservative LMI characterizations and much wider scope of the applicability. Furthermore, the results are extended to H(∞) state feedback synthesis. Finally, two numerical examples illustrate the superiority and effectiveness of the new results.
本文研究了一类基于连续时间仿射模糊模型的非线性系统的状态反馈控制器设计问题。提出了一种基于新的扩张线性矩阵不等式（LMI）刻画的凸分段仿射控制器设计方法，其中系统矩阵与李雅普诺夫矩阵分离，使得控制器参数化与李雅普诺夫矩阵无关。与现有工作相比，所得到的稳定性条件导致了更少保守的 LMI 刻画和更广泛的适用性范围。此外，将结果扩展到 H(∞)状态反馈综合。最后，两个数值例子说明了新结果的优越性和有效性。
