Discrete-time adaptive sliding mode control for a class of uncertain time delay systems

This paper is concerned with a discrete-time adaptive sliding mode control for a class of uncertain time delay systems. It is assumed that the dynamic systems are described by a discrete-time time delay state equation with mismatched uncertainties, and that the states are measured in the contamination with independent random noises. The augmented state equations are derived based on the state of the time delay, and the weighted extended Kalman filter and the weighted least squares estimator to take the estimates for the augmented states and the uncertainties are proposed. The discrete-time adaptive sliding mode control is designed using the integral-type sliding surface and the output information obtained from the estimators. It is verified that the estimation errors converge to zero as time increases, and the states for the dynamic systems are ultimately bounded under the action of the proposed adaptive sliding mode control. The effectiveness of the proposed method is indicated by the simulation experiment in a simple numerical example.