Chattering reduction in the variable structure control of nonlinear systems with incomplete state availability

In this paper the robust stabilization problem for a class nonlinear systems with incomplete state availability is addressed and solved by using a second order sliding mode approach. In previous works a discontinuous control input that guarantees the asymptotic stabilization of a class of systems expressed in the Brunowsky normal form, in which the last state variable was assumed to be not measurable, has been derived. The aim of the present paper is to exploit the on-line approximate availability of the equivalent control, obtained by means of a suitable filtering procedure, in order to improve the accuracy and to reduce the amplitude of the discontinuous control effort. As a result, the actual control has two components: the first one is continuous, while the second one is discontinuous with arbitrarily-small magnitude. Simulation results are provided to show the effectiveness of the proposed scheme.