We obtain sufficient criteria for simplicity of systems, that is, rings R that are equipped with a family of additive subgroups R-s for s is an element of S, where S is a semigroup satisfying R = Sigma (s is an element of S) R-s and RsRt subset of R-st for s, t is an element of 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 R-s subset of R-t for all s, t is an element of S with s <= t and for each s is an element of S, the RsRs*-Rs*Rs -bimodule R-s is s-unital. As an application, we obtain generalizations of recent criteria for simplicity of skew inverse semigroup rings by Beuter, Goncalves, Oinert and Royer, and then for Steinberg algebras over non-commutative rings by Brown, Farthing, Sims, Steinberg, Clark and Edie-Michell.