A remark on passivity-based and discontinuous control of uncertain nonlinear systems

We address the problem of robust stabilisation of nonlinear systems a!ected by time-varying uniformly bounded (in time) a$ne perturbations. Our approach relies on the combination of sliding mode techniques and passivity-based control. Roughly speaking we show that under suitable conditions the sliding mode variable can be chosen as the passive output of the perturbed system. Then we show how to construct a controller which guarantees the global uniform convergence of the plant's outputs towards a time-varying desired reference, even in the presence of permanently exciting time-varying disturbances. We illustrate our result on the tracking control of the van der Pol oscillator. 2001 Published by Elsevier Science Ltd.