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.