The exponential formula for a Lipschitz differential inclusion

The differential inclusion formulation subsumes certain control problems. The process of converting the control formulation into a differential inclusion can also be reversed while at the same time preserving the essential character of the assumptions. Hence there is no essential difference in studying problems in either form. However, the differential inclusion has a simplified mathematical formulation, and indeed resembles an ordinary differential equation. It is shown that the Euler method of successive approximations from ordinary differential equation theory is applicable to set-valued problems as well. This is not so easily stated using the control formulation, but in terms of differential inclusions it can be written succinctly