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

We address the problem of robust stabilisation of nonlinear systems affecte d by time-varying uniformly bounded (in time) affine perturbations. Our app roach relies on the combination of sliding mode techniques and passivity-ba sed control. Roughly speaking we show that under suitable conditions the sl iding mode variable can be chosen as the passive output of the perturbed sy stem. Then we show how to construct a controller which guarantees the globa l uniform convergence of the plant's outputs towards a time-varying desired reference, even in the presence of permanently exciting time-varying distu rbances. We illustrate our result on the tracking control of the van der Po l oscillator. (C) 2001 Published by Elsevier Science Ltd.