Static sliding-motion phenomena in dynamical systems

Abstract

We present a new type of sliding motion which results from a novel choice of the sliding surfaces. We suggest to define these such that they become explicitly dependent on the outputs of the discontinuous block. We prove that, under this design, a special sliding mode characterizes 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 on when this dynamical behavior begins and continues its motion in static sliding mode. We show and simulate a control application in robust stabilization of nonlinear systems.