Discretisation method and stability criteria for non-linear systems under discrete-time time delay control

Time delay control (TDC) for non-linear systems has rapidly drawn attention as a result of its unusually robust performance and yet its extraordinarily compact form. In many real applications, TDC has been implemented digitally and the time delay, λ, was set to the sampling period of the control system, which is a constant during the control process. The existing stability analysis, however, has been made based on the assumption of the continuous-time TDC and infinitesimal time delay (λλ0). The assumption not only fails to reflect the reality that the closed-loop system (CLS) is a sampled-data system, but also leads to a stability criterion in which important parameters, such as λ, are absent. In this paper, therefore, sufficient stability criteria for a non-linear system based on the premise of discrete-time TDC and λ that is equal to the sampling period are presented. To this end, we have first proposed a discretization method to derive the approximate discrete-time model of CLS. Then by using the model and the concepts of consistency and Lyapunov stability, we have derived stability criteria for the exact discrete-time model of CLS. The suggested criteria consist of the sampling period and other parameters of TDC. These criteria have been verified by simulation results.