Parameters estimation using sliding mode observer with shift operator

In the control system's literature, one can find considerable amount of research in the area of system parameters identification. Most of these techniques are based on minimizing the estimation error in some statistical framework such as least square error based methods. In most cases, using these techniques, one can prove the uniform exponential stability of the state and parameter estimation error, but the convergence rate can be too low. However, when designing control systems, knowledge of unknown immeasurable (or even time varying) parameters might be crucial for the operation of the controller and thus have to be accurately estimated with a desired rate of convergence. In this paper, we demonstrate a way to provide an estimation technique with tunable convergence rate using sliding mode with linear operators such as time delay.