On the dynamical sliding mode control of nonlinear systems

Abstract

The consequences of the differential algebraic approach in the sliding mode control of nonlinear single-input single-output systems are reviewed in tutorial fashion. Input-dependent sliding surfaces, possibly including time derivatives of the input signal, are shown to arise naturally from elementary differential algebraic results pertaining to the Fliess's Generalized Controller Canonical Forms of nonlinear systems. This class of switching surfaces generally leads to chattering-free dynamically synthesized sliding regimes, in which the highest time derivative of the input signal undergoes all the bang-bang type discontinuities. Examples illustrating the obtained results are also included.