Control scheme for LTI systems with Lipschitz non-linearity and unknown time-varying input delay

In this study, the authors propose a control structure for a class of linear time-invariant (LTI) systems with Lipschitz non-linearity and unknown time-varying input delay. This scheme considers the worst-case scenario in control design with truncated prediction feedback approach, and takes into account the information of the lower bound of delay in the stability analysis. A finite-dimensional controller is constructed, requiring neither the non-linear function nor the exact delay function. The truncated prediction deviation is minimised by employing the delay range, and then bounded by integral construction and related techniques. Within the framework of Lyapunov-Krasovskii functionals, sufficient delay-range-dependent conditions are derived for the closed-loop system to guarantee the global stability. Two numerical examples are given to validate the proposed control design.