Robust Elimination Lemma: Sufficient Condition for Robust Output Feedback Controller Design

A linear algebra result known as Elimination lemma is frequently used in lot of filtering and control problems to transform products of unknown matrices to LMI form, however, the robust counterpart to elimination lemma is not known. In this paper, sufficient robust stability condition inspired by elimination lemma is developed and the respective robust static output feedback controller design procedure based on LMI formulation and solution is proposed. The proposed robust controller design procedure is computationally not demanding and is illustrated on example.