Global Stabilization by Memoryless Feedback for Nonlinear Systems With a Limited Input Delay and Large State Delays

This article studies the problem of global asymptotic stabilization (GAS) by memoryless state and/or output feedback for a family of nonlinear systems with delays in the state and input. Under a linear growth condition, together with the lower-triangular bounding requirement, it is proved that GAS of the time-delay nonlinear system under consideration is achievable by memoryless state and output feedback, respectively, as long as the input delay is limited. With the aid of the Lyapunov-Krasovskii stability theorem and the feedback domination design approach, we construct, step-by-step, a set of Lyapunov-Krasovskii functionals and memoryless state and/or output feedback controllers, achieving GAS of the closed-loop systems with delays. Extensions to nonlinear systems with inverse dynamics are also included.