Universal stabilisation design for a class of non‐linear systems with time‐varying input delays

The authors consider a universal stabilisation design for a class of non‐linear systems with time‐varying input delays in this study. Using the transport partial differential equation to express the delay, stability analysis is conducted with infinite‐dimensional backstepping transformations and by constructing a Lyapunov functional. Sufficient conditions are obtained, and a universal stabilisation formula is presented. Moreover, the stabilisation formula is optimal with respect to a meaningful cost functional. Finally, three examples are given to illustrate the effectiveness of the proposed design technique.