Robustness and Stability Analysis of Time Delay Control

This paper proposes a modified Time Delay Controller for a class of uncertain nonlinear system. The controller uses delayed inputs and delayed derivative of some of the state variables to estimate the uncertain dynamics. To attenuate the noise amplified by the differentiation, the delay time is chosen to be much larger than the sampling period. Keeping the delay time at an appropriate level, the performance of the system is improved significantly by reducing the sampling period without further amplifying high-frequency noise. The analysis on a special class of systems shows that robustness to variation of the input matrix is also enhanced much further by the scheme. Since the estimation is updated at a sampling period much shorter than the observation period (the delay time), the control input which contains the estimated dynamics changes more smoothly with time, compared to the case when the sampling period is the same as the delay time.