Chattering-free sliding mode control for linear uncertain systems with multiple time-delays

This paper considers the sliding mode control for linear uncertain systems with multiple time-delays. A new chattering-free sliding mode control law is designed with saturation function instead of sign function for time-delay systems. The control algorithm divides the control process into two phases. When the system trajectory is outside of the given the boundary layer, the chattering-free control law is used to drive the trajectory converged to the boundary layer. When the trajectory is inside the boundary layer, by choosing the appropriate width of the boundary layer, the asymptotically stable of the system can be guaranteed. This control algorithm eliminates the sliding-mode chattering caused by the discontinuity of traditional SMC law for the uncertain time-delay system. The numerical simulation validates the proposed approach.