Global stabilisation of nonlinear systems with unknown time-varying delay and measurement uncertainty

Based on a new constructive solution of a couple of matrix inequalities containing an unknown time-varying parameter, this paper proposes a novel dual-gain scaling approach including a dynamic-gain observer and an output feedback controller with static and dynamic gains. In particular, our control approach is applicable to a class of nonlinear time-delay systems with nonlinear growth constraint and large unknown measurement sensitivity that may be non-differentiable. With the help of the Razuminkhin theorem, it is shown that the global adaptive stability of the resulting closed-loop system is achieved and our controller is robust to arbitrary bounded time-varying delay. In addition, the control approach proposed is non-backstepping and has low computing complexity.