Abstract: Dynamic output feedback control via GKYP lemma with small gain specification does not automatically guarantee the stability of the resulting closed-loop systems. Improvements are made to the existing approach to render the asymptotical stability, and the new approach is applied to researching the tracking problem. For the synthesis problem with finite frequency small gain specification via dynamic output feedback control, this paper adds a stability constraint to the design in terms of Linear Matrix Inequality（LMI）, without adding any new variables. Furthermore, for the situation that feasible solution can not be found after adding the stability constraint, based on the non-uniqueness of the null space condition, it provides an alternative null space condition to enlarge the feasibility region of this design. Simulation example in tracking problem shows that, although dynamic output feedback control in finite frequency range is conservative, by choosing basis matrix reasonably, the degree of conservatism can be smaller than that of optimal H∞ control in entire frequency range.

Key words: stability, dynamic output feedback, finite frequency range, Generalized Kalman-Yakuborich-Popov（GKYP） lemma, tracking problem, null space

摘要： 基于GKYP引理的动态输出反馈设计，未保证设计后闭环系统的稳定性。针对以小增益作为指标的有限频段动态输出反馈问题，在不增加新变量的前提下，增加稳定性约束，使得设计后的闭环系统渐近稳定且满足有限频段性能指标。针对增加约束后难以找到可行解的情况，基于零空间条件的不惟一性，补充了另一种零空间条件，从而扩大了问题的可行域。将改进后的方法应用于有限频段跟踪问题的研究，通过仿真例子验证，有限频段动态输出反馈虽然存在保守性，但在合理选择基矩阵R的情况下，仍然可以使得其保守性小于传统的全频段最优H∞控制的保守性。

关键词: 稳定性, 动态输出反馈, 有限频段, 广义的卡尔曼-雅可波维奇-波波夫引理（GKYP）, 跟踪问题, 零空间