We obtain sufficient criteria for simplicity of systems, that is, rings R that are equipped with a family of additive subgroups Rs for s∈S, where S is a semigroup satisfying R=∑s∈SRs and RsRt⊆Rst for s,t∈S. These criteria are specialized to obtain sufficient criteria for simplicity of what we call s-unital epsilon-strong systems, that is, systems where S is an inverse semigroup, R is coherent, in the sense that Rs⊆Rt for all s,t∈S with s≤t and for each s∈S, the RsRs∗-Rs∗Rs-bimodule Rs is s-unital. As an application, we obtain generalizations of recent criteria for simplicity of skew inverse semigroup rings by Beuter, Gonçalves, Öinert and Royer, and then for Steinberg algebras over non-commutative rings by Brown, Farthing, Sims, Steinberg, Clark and Edie-Michell.