一类线性时滞系统的状态反馈H_∞控制器设计

State Feedback H_∞ Controller Design for a Class of Linear Delayed Systems

研究线性时滞系统的状态反馈H∞ 控制器设计问题·在状态和控制同时存在时滞以及控制输出方程具有更一般形式的情况下 ,以线性矩阵不等式的形式给出了系统存在状态反馈H∞ 控制器的充分条件·当这个条件成立时 ,利用线性矩阵不等式的解可以构造状态反馈控制律 ,使得闭环系统渐近稳定 。

The state feedback H ∞ controller design problem for linear delayed systems was studied. In the case that delay exists in state and control simultaneously and the controlled output equation has general form, a sufficient condition for the existence of state feedback H ∞ controllers is given in terms of a linear matrix inequality. When the condition is fulfilled,a state feedback control law can be constructed based on the solutions of the linear matrix inequality, which guarantees the asymptotic stability of the closed loop control systems and reduces the effect of the disturbance input on the controlled output to a prescribed level. The proposed method is applied to linear systems with multiple state delays and multiple control delays.