This unique monograph introduces an important new area of control system research and presents some new methods for solving some typical problems in the field of sandwich nonlinear systems. Sandwiched nonsmooth nonlinearities such as dead-zone, hysteresis and backlash between dynamic blocks are presented, as well as continuous-time control designs. A framework for hybrid control is developed that is used to design control schemes for different cases of the control problem with required modifications. Friction compensation is addressed for systems with sandwiched friction along with sandwiched dynamics. An open problem of the control of sandwich nonlinear systems with actuator failures is introduced by a control design for an illustrative case.