不确定离散线性系统的鲁棒镇定

Robust Stabilization of Uncertain Discrete-time Linear Systems

针对一类具有范数有界时变不确定性的离散线性系统，研究其二次稳定化状态反馈控制律的设计问题。推导出二次稳定化控制律存在的一个充分必要条件，该条件被进一步等价地表示成一个线性矩阵不等式的可解性问题。后者可用现有方法方便地求解，且它的解提供了所有二次稳定化控制律的一个参数化表示。

This paper studies a problem of designing quadratic stabilizing state feedback controllers for a class of discrete-time linear systems suffering from uncertainty of the norm-bounded time-varying type. A necessary and sufficient condition for the existence of such controllers is derived, and it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality(LMI). The latter can be solved by using the existing efficient convex optimization techniques and its solutions provide a parametrized representation of all quadratic stabilizing controllers.