模糊不确定时滞系统的保成本控制

Guaranteed Cost Control for Uncertain Fuzzy Systems with Time-delays

讨论了基于T-S模型的不确定时滞系统的保成本控制问题。文章采用并行补偿状态反馈控制方法和时滞相关稳定性分析方法,通过引入一个带调节因子的Lyapunov-Krasovskii泛函,利用线性矩阵不等式的形式给出了状态反馈控制器存在的充分条件。当调节因子取不同值时,最小保成本值和反馈增益也是不同的,不同的反馈增益导致不同的动态性能,因此,可以通过选取合适的调节因子来优化闭环系统的动态性能。最小保成本值可以看作调节因子的函数,因此,可以通过求解一个凸优化问题来求得最小的保成本值和最优的调节因子,文章给出了一个求解最小保成本值的算法。并利用仿真示例验证了所给方法的有效性。

The guaranteed cost control problem for uncertain nonlinear systems with time-delay which can be represented by Takagi-Sugeno （T-S） fuzzy model is surveyed. The parallel distributed compensation （PDC） control method and delay-dependent stability analysis method are adopted to study the stabilization of systems. By introducing a new Lyapunov-Krasovskii functional with adjustable parameters, some sufficient conditions for the existence of state feedback controller are given in the form of linear matrix inequalities （LMIs）. Different guaranteed cost and different feedback gains can be gotten by choosing different adjustable parameters. Different feedback gains lead to different dynamic performance of closed-loop systems, therefore, the optimal dynamic performance of closed-loop systems and lower guaranteed cost can be gotten by choosing proper adjustable parameters, and an algorithm is given to get the minimum of guaranteed cost. The effectiveness of the proposed method can be illustrated by the simulation example.