Integral sliding mode control of time-delay systems with mismatching uncertainties

A linear matrix inequality (LMI)-based sliding surface design method for integral sliding mode control of uncertain time-delay systems with mismatching uncertainties is proposed. The uncertain time-delay system under consideration may have mismatching norm bounded uncertainties in the state matrix as well as the input matrix. A sufficient condition for the existence of a sliding surface is given to guarantee asymptotic stability of the full order sliding mode dynamics. An LMI characterization of the sliding surface is given, together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time. Finally, a simulation is given to show the effectiveness of the proposed method.