Structure of state feedback with K-out-of-M integrity

Abstract This paper is concerned with the structure of reliable state feedbacks. In this paper, the rank of state feedback gains which attain quadratic stability for k failures out of m suspected actuators is investigated. This paper reveals a class of LMI problems for which robust elimination lemma holds, and also gives a conjecture that the rank of state feedback gains can be restricted without performance deterioration. This conjecture suggests the essential cause of the trade-off between the achievable performance and the reliability against failures.