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

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