This lecture presents the current state-of-the-art in the study of input delay tolerance of nonlinear control systems.
In the first part of this talk, we focus on the problem of semiglobal input delay tolerance (SGIDT) under smooth feedback. A semiglobal control framework is introduced for the analysis/synthesis of input delay tolerance of nonlinear systems under smooth feedback. Using the converse Lyapunov theorem on global asymptotic local exponential stability (GALES), together with the Razumikhin theorem, we prove that: 1) GALES implies the SGIDT of nonlinear systems under smooth state feedback; 2) GALES and uniform observability imply the SGIDT of MIMO nonlinear systems under smooth output feedback.
In the second part of this talk, we concentrate on the problem of global input delay tolerance (GIDT) under nonsmooth feedback for nonlinear systems that are not LES nor smoothly stabilizable. Using the homogeneous systems theory, we further prove that homogeneity of degree zero and global stabilizability by homogeneous feedback imply global input delay tolerance. Various examples and counter-examples are also presented to illustrate some fundamental limitations in achieving SGIDT under smooth feedback or GIDT under nonsmooth feedback.