Robust stabilisation of uncertain time-delay dynamical systems with unknown bounds of uncertainties: a non-linear control method

In this study, the problem of robust stabilisation is considered for a class of uncertain dynamical systems with state delays. Here, it is assumed that the upper bounds of the delayed state perturbations, uncertainties and external disturbances are completely unknown. For such a class of uncertain time-delay dynamical systems, a novel design method is presented in which a class of continuous memoryless robust stabilising controllers is constructed. In particular, by making use of the presented method, it is not required to introduce some adaptive schemes to update the unknown upper bounds, which makes the control schemes simpler than adaptive robust control schemes reported in the control literature. Moreover, such a control scheme proposed in this study will be called adaptation-free robust control scheme. It is also shown that the solutions of the resulting closed-loop time-delay dynamical systems can be guaranteed to be uniformly ultimately bounded. Finally, the simulations of some numerical examples are provided to demonstrate the validity of the theoretical results.