离散T-S模糊系统状态反馈最优H∞控制器设计

State feedback optimal H_∞ controller design for discrete-time T-S fuzzy systems

为了研究离散T-S模糊控制系统的状态反馈H∞控制问题。考虑了受控输出中输入变量系数不为零的情况,对离散T-S模糊控制系统系统提出了一状态反馈最优H∞控制的新方法,基于系统状态完全可以测量的前提下,把闭环系统的扰动抑制度γ的最优问题转化为一个矩阵的最大特征值的最小化问题;同时通过相关的LMI定理,把H∞控制器增益存在的充分条件归结为一组线性矩阵不等式(LMI)问题,该线性矩阵不等式问题可以通过凸优化技术得以解决,给出的结果更具一般性意义。此外,利用隶属度函数的特点近一步降低了控制器增益存在的条件的保守性。最后,一个具体的仿真例子说明了该算法的可行性。

The problem of state feedback H∞ control for discrete-time T-S fuzzy control systems is studied, and the case that coefficients of input variables in controlled output are nonzero is taken into full consideration. A new method is proposed to deal with state feedback optimal H∞ control of discrete-time T-S fuzzy control systems. Under the condition of measurable system states, the problem of minimizing the disturbance restraining degree γ is translated into the problem of minimizing the maximum eigenvalues of a special matrix, and the existence conditions of H∞ controller gain are transferred into an LMI problem, which can be solved by convex optimization. The derived results are more general than the existing ones. The characters of membership functions are made full use of to reduce the conservatism of the obtained results. Finally, the effectiveness of the proposed approach is shown through a numerical example.