T-S模糊时滞系统的鲁棒无源控制

Robust passive control for T-S fuzzy systems with time-varying delays

基于Lyapunov稳定性理论,对具有参数不确定性的T-S模糊时滞系统的鲁棒稳定性和无源性进行了研究。具有参数不确定性的T-S模糊模型可以任意精度近似连续非线性不确定系统。假设系统中的参数不确定性是范数有界的。运用Lyapunov稳定性理论给出了鲁棒无源控制器存在的充分条件。通过解一组线性矩阵不等式(LMIs),可直接获得鲁棒无源控制器。所设计的鲁棒无源控制器能够保证对于T-S模糊时滞系统中所有的参数不确定性,闭环系统都是鲁棒稳定的并且是严格无源的。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。数值例子验证了所提出设计方法的有效性。

The passive analysis and control synthesis of Takagi-Sugeno （T-S） fuzzy systems with time-varying delays based on Lyapunov stability theoty is investigated. Takagi-Sugeno （T-S） fuzzy systems with timevarying delays can approach any continuous functions at any precision. The parametric uncertainty is assumed to be norm bounded. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequalities（LMIs）, robust passive controllers are designed such that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example demonstrates the effect of the proposed design method.