  The paper introduces notions of robustness margins geared towards the
analysis and design of systems that switch and oscillate. While such phenomena
are ubiquitous in nature and in engineering, a theory of robustness for
behaviors away from equilibria is lacking. The proposed framework addresses
this need in the framework of p-dominance theory, which aims at generalizing
stability theory for the analysis of systems with low-dimensional attractors.
Dominance margins are introduced as natural generalisations of stability
margins in the context of p-dominance analysis. In analogy with stability
margins, dominance margins are shown to admit simple interpretations in terms
of familiar frequency domain tools and to provide quantitative measures of
robustness for multistable and oscillatory behaviors in Lure systems. The
theory is illustrated by means of an elementary mechanical example.
