Static sliding-motion phenomena in dynamical systems

We present a new type of sliding motion which results from a novel choice of the sliding surfaces. We define these sliding surfaces such that they become explicitly dependent on the outputs of the discontinuous block. We prove under this design, a special sliding mode characterises the system dynamics, which we name static sliding mode, because it occurs along a static contour of the closed-loop system. We give constructive conditions when this dynamical behavior begins and continues its motion in a static sliding mode. We show and simulate a control application in robust stabilization of nonlinear systems.