离散T-S模糊系统的鲁棒无源控制

Robust passive control for discrete-time T-S fuzzy systems

通过应用Lyapunov稳定性理论,研究了具有参数不确定性的离散T-S模糊系统的鲁棒稳定性和无源性。假设系统中的参数不确定性是范数有界的。具有参数不确定性的T-S模糊模型可以以任意精度近似非线性不确定系统。利用Lyapunov稳定性理论给出了鲁棒无源控制器存在的充分条件。通过运用线性矩阵不等式方法设计出的鲁棒无源控制器能够保证对于T-S模糊系统中所有的参数不确定性闭环系统都是稳定的并且满足给定的无源性能指标。并且,通过求解带有约束条件的线性矩阵不等式问题,可以设计出具有最大耗散率的鲁棒无源控制器。数值算例证明了所提出的设计方法的有效性。

Robust stability analysis and passivity for discrete-time Takagi-Sugeno （T-S） fuzzy systems with parametric uncertainties was studied via Lyapunov stability theory. Under the assumption of norm bounted parametric uncertainty, the T-S fuzzy model can approximate nonlinear uncertain systemsa at any precision. On the basis of Lyapunov stability theory, a sufficient condition on the existence of robust passive controllers was derived. With linear matrix inequality （LMI） method, robust passive controllers were designed such that for all admissible uncertainties the closed-loop system is robust stable and strictly passive. The robust passive controller design was parameterized in term of LMI problem. Furthermore, a convex optimization problem with LMI cnstrains was formulated to design robust passive controllers at maximum dissipation rate. A numerical example demonstrates the effect of the proposed design method.