A nonsmooth analysis and synthesis for semiglobal input delay tolerance of nonlinear systems without LES

This research focuses on the input delay tolerance problem for C0 yet possibly non-locally Lipschitz continuous nonlinear systems that are not locally exponentially stabilizable (LES) by any smooth feedback. Using the Lyapunov–Razumikhin method, nonsmooth analysis/synthesis tools and homogeneity with respect to a family of dilations, we show that global asymptotic stabilizability (GAS) by nonsmooth homogeneous state feedback implies semiglobal asymptotic stability (SGAS) of the closed-loop system with input delay — the property of semiglobal input delay tolerance (SGIDT), if the C0 nonlinear systems are homogeneous with positive degree. In the case of output feedback, we prove that the SGIDT property still holds for the same class of nonlinear systems if they are GAS by homogeneous output feedback. As a byproduct of these developments, new SGIDT results under nonsmooth feedback are obtained for significant classes of inherently nonlinear systems with actuator delay.