Sliding mode control of uncertain dynamical systems with time delay using the continuous time approximation method

A study of sliding mode control of uncertain dynamical systems with time delay is presented in this paper. The systems are assumed to have constant delay time and uncertain parameters with known upper and lower bounds. The method of continuous time approximation is applied to formulate the sliding mode control problem. The proposed treatment of the control delay leads to a higher-order control formulation for a system with additive uncertainties only. An optimal sliding surface is designed such that on the sliding surface, the controlled state variables act like a feedback control to the uncontrolled state variables. Examples of non-linear systems are presented to demonstrate the theoretical work.