  Robust global stabilization of nonlinear systems by observer-based feedback
controllers is a challenging task. This article investigates the problem of
designing observer-based stabilizing controllers for incrementally quadratic
nonlinear systems with external disturbances. The nonlinearities considered in
the system model satisfy the incremental quadratic constraints, which are
characterized by incremental multiplier matrices and encompass many common
nonlinearities. The simultaneous search for the observer and the controller
gain matrices is formulated as a feasibility problem of linear matrix
inequalities, for two parameterizations (i.e., the block diagonal
parameterization and the block anti-triangular parameterization) of the
incremental multiplier matrices, respectively. The closed-loop system
implementing the observer-based feedback controller is proven to be
input-to-state stable with respect to external disturbances. Using the proposed
continuous-time observer-based controllers, event-triggered controllers with
time regularization are constructed for globally Lipschitz systems, such that
the closed-loop system is Zeno-free and input-to-state practically stable.
