Stability analysis of discrete time delay control for nonlinear systems

This paper presents a solution to the long standing problem of the stability of Time Delay Control (TDC) for nonlinear systems. Ever since it was first introduced, TDC has rapidly drawn attentions owing to its unusually robust performance and yet its extraordinarily compact form. The existing stability analyses have been made based on the assumption that the TDC is continuous and time delay L → 0. The assumption, however, not only fails to reflect the reality that TDC is usually implemented in a digital processor, but also leads to a stability criterion in which important parameters, such as L, that play crucial roles are absent. In this paper, therefore, we present our theoretical investigation on the stability of TDC with the premise that TDC is discrete and L is nonzero and finite. Specifically, stability criteria based on the premise are derived, so that one may clearly grasp which parameters affect stability and how. For the analysis of the closed-loop stability, we have first derived its approximate discrete model (approximate discrete plant model with the discrete TDC). Then by using the model and the concepts of consistency and Lyapunov stability, we have analyzed the stability of the exact discrete model of closed loop systems. The analysis results in a stability criteria consisting of L and other parameters that affect the performance of TDC. The suggested stability analysis has been verified by simulation results.