The minimum gain lemma

This paper focuses on the newly developed notion of minimum gain and the corresponding Large Gain Theorem. The Large Gain Theorem is an input–output stability result particularly well suited to unstable plants connected in feedback with stable or unstable controllers. This paper aims to facilitate the practical application of these results. An altered definition of minimum gain broadens the applicability of the Large Gain Theorem, and the novel Minimum Gain Lemma provides LMI conditions that imply and are often equivalent to a minimum gain for LTI systems. Numerical examples are provided to clarify the differences between the existing and proposed definitions of minimum gain, highlight the utility of the newly established Minimum Gain Lemma, and demonstrate how the paper's contributions may be employed in practice. Copyright © 2014 John Wiley & Sons, Ltd.