On the robustness of variable structure systems in the presence of measurement noise

Sliding mode control systems provide an effective and robust means of controlling nonlinear plants. The main advantage of the systems is their insensitivity to disturbance and parameter uncertainties. However, for several reasons, the advantage is usually not perfectly achieved in the real systems. One of the reasons why the real systems are not fully insensitive to disturbance and parameter uncertainty is the presence of the measurement noise in the systems. In this paper the effect of the noise on the robustness of variable structure control is analysed. It is shown, that on the contrary to the ideal circumstances, when the measured state is corrupted with noise, variable structure control may not be able to force the state of the controlled plant onto the switching surface itself, but only to some vicinity of the surface. The vicinity is determined in the paper