Homogeneous output feedback design for time-delay nonlinear integrators and beyond: An emulation

Abstract

Global asymptotic stabilization (GAS) of a chain of nonlinear integrators with large constant delays in state and input is shown to be achievable via memoryless output feedback, although its linearization even without delays is uncontrollable and unobservable. The proof is constructive and carried out by designing a delay-free, reduced-order homogeneous observer and a homogeneous controller, which rely on the Lyapunov–Krasovskii functional stability theorem, a homogeneous domination design, and an emulation approach. As a byproduct of the development, GAS by memoryless homogeneous output feedback is also proved to be possible for a class of time-delay upper-triangular systems with strong nonlinearity.