Global adaptive output feedback control of nonlinear time-delay systems with measurement uncertainty

In this paper, a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems with multiple unknown time delays. By constructing Lyapunov–Krasovskii functionals, it shows that global state asymptotic regulation can be ensured by introducing a single dynamic gain; furthermore, global asymptotic stabilization can be achieved by choosing a sufficiently large static scaling gain when the upper bounds of all system parameters are known. Especially, the output coefficient is allowed to be non-differentiable with unknown upper bound. This paper proposes a generalized Lyapunov matrix inequality based dynamic-gain scaling method, which significantly simplifies the design computational complexity by comparing with the classic backstepping method.