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A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface sx(t)=0 in the system state space, with s/spl dot/x(t) identically equal to zero, a regime enforced by a control signal depending on sx(t), but directly acting only on s/spl uml/x(t)). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.
Bartolini et al. (Sat,) studied this question.