Global Input Delay Tolerance of MIMO Nonlinear Systems under Nonsmooth Feedback: A Homogeneous Perspective

Abstract

In this paper, we tackle the problem of when a globally asymptotically stabilizable (GAS) nonlinear system by either state or output feedback is globally tolerable with respect to input delay. We focus on the case when the continuous system is not stabilizable by linear or smooth feedback, and thus local exponential stabilizability (LES) is not fulfilled. With the aid of the Lyapunov-Krasovskii functional method and weighted homogeneity, we prove that for a multi-input-multi-output (MIMO) nonlinear system with homogeneous degree zero, global asymptotic stabilizability by nonsmooth but Hölder continuous state or output feedback implies global asymptotic stability (GAS) of the closed-loop system with input delay, i.e., the property of global input delay tolerance (GIDT). We then illustrate applications of the obtained GIDT results to significant classes of time-delay nonlinear systems with uncontrollable/unobservable linearization, including but not limited to a chain of nonlinear integrators, higher-order systems with a lower-triangular or upper-triangular structure, and beyond.