一类模糊时滞系统指定衰减度的鲁棒控制

Robust controller with definite attenuation for a class of fuzzy time-delay systems

研究了一类非线性时滞系统基于模糊T-S模型的鲁棒镇定问题,所考虑的不确定时滞系统含有时变未知但有界的状态时滞,首先利用Razumikhin定理和Lyapunov定理,得出了由模糊T-S模型描述的非线性时滞系统鲁棒稳定且具有指定衰减度的判据,其次得到了具有指定衰减度的无记忆状态反馈控制律存在的充分条件及相应的控制器设计方法,该条件被进一步等价地转化为一个线性矩阵不等式的可解性问题,所设计的控制器确保了闭环系统具有指定衰减度鲁棒稳定。

The problem of robust stabilization for nonlinear time-delay system based on fuzzy T-S model is developed in this paper. The systems under consideration include time-varying unknown but bounded time-delay in state. Firstly, by applying the Razumikhin theory and Lyapunov theory, a criterion of robust stability with definite attenuation for nonlinear time-delay system is derived. Secondly, the sufficient condition for the existence of memoryless state feedback controller with definite attenuation and the method of designing controller are derived. The condition is also further equivalent to the solvability of certain linear matrix inequality （LMI）. The designed controller guarantees the closed-loop system to possess robust stability with definite attenuation.