Sensitivity analysis of composite piecewise smooth equations

This paper is a contribution to the sensitivity analysis of piecewise smooth equations. A piecewise smooth function is a Lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible B-derivative at this point. We emphasise the role of functions of the type f = g ° h where g is piecewise smooth and h is smooth and present verifiable conditions which ensure that the function f = g ° &htilde; is a Lipschitzian homeomorphism near a given point for every &htilde; sufficiently close to h with respect to the C¹-topology.