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利用有界实引理和线性矩阵不等式技术,得到了连续时间正系统静态输出反馈H_∞控制问题可解的一个充要条件。在此基础上给出了连续时间正系统存在静态输出反馈鲁棒H_∞控制器的一个充分条件,所得条件均由带有矩阵等式约束的线性矩阵不等式给出。H_∞控制器增益矩阵可利用锥补线性化技巧来求解。最后,作为静态输出反馈的一种特殊情形,得到了状态反馈控制器存在的一个充分条件,并通过数值仿真验证了结论的正确性。
By using bounded real lemmas and linear matrix inequalities, a necessary and sufficient condition for the solvability of the system output feedback H_∞ control for continuous time systems is obtained. On this basis, a sufficient condition for a robust H ∞ controller with static output feedback is given for a continuous-time positive system. The obtained conditions are given by the linear matrix inequalities with matrix equality constraints. The H_∞controller gain matrix can be solved by using the cone linearization technique. Finally, as a special case of static output feedback, a sufficient condition for the existence of state feedback controller is obtained. The correctness of the conclusion is verified by numerical simulation.