受控正系统的弹性静态输出反馈鲁棒H_∞控制

Resilient static output feedback robust H_∞ control for controlled positive systems

首先,利用线性矩阵不等式(LMI)及有界实引理,借助一个小的标量,得到了受控正系统弹性静态输出反馈鲁棒H∞控制的一个充分条件,使得控制器参数与未知参数分开,从而更有利于弹性静态输出反馈控制器的设计.然后,基于此条件,针对控制矩阵的一种特殊情形给出了一个推论,并得到了更一般的受控正系统弹性静态输出反馈鲁棒H∞控制的充分条件,其中的控制器增益矩阵均可根据锥补线性化技巧来进行求解.最后,利用数值仿真表明了结论的有效性.

Firstly, by means of a small scalar, a sufficient condition of resilient static output feedback robust H~ control for controlled positive systems is obtained via linear matrix inequality （LMI） and bounded real lemma, which is useful for the design of resilient static output feedback controller because the controller parameter is separated from the unknown parameter. Then, based on the above condition, an inference for the special case of the control matrix is given and a sufficient condition of resilient static output feedback robust H~ control for more general controlled positive systems is established. Furthermore, the desired controller gain matrix can be derived via the cone complementarity linearization techniques directly. Finally, a numerical simulation to show the validity of the results is presented.