A robust sliding mode controller for nonlinear systems with mismatched perturbations

For many control systems the presence of perturbations may decrease performance, so that their rejection has been an area of active research for the last decades. Roughly speaking, there are two kind of perturbations, those which are matched, i.e. the control input can act directly on them, and those which are mismatched, i.e. the control input cannot act directly on them. While there are many solutions for the first case, the second one remains a challenge. This note improves a former result by the authors to avoid singularities in a Sliding Mode Control (SMC) approach which provides ultimate boundedness of the desired output with an ultimate bound that can be made arbitrarily small. Simulation results are provided to validate the introduced theory.