Optimal sliding mode control for uncertain systems with time delay

This paper considers the sliding mode control for linear systems with time-delay affected by uncertainties. By using the successive approximation approach, a novel time-varying sliding surface is designed in an optimal fashion. The stability of the sliding mode is analyzed. The switching manifold assures that the state trajectories of the closed-loop system converge to zero. The convergence speed of every state trajectory on the ideal sliding surface can be adjusted through choosing the parameters of the quadratic performance index. A disturbance observer is constructed to make the control input physically realizable. A numerical simulation is given to show the effectiveness of the proposed design approach.