  This letter presents a framework for synthesizing a robust full-state
feedback controller for systems with unknown nonlinearities. Our approach
characterizes input-output behavior of the nonlinearities in terms of local
norm bounds using available sampled data corresponding to a known region about
an equilibrium point. A challenge in this approach is that if the
nonlinearities have explicit dependence on the control inputs, an a priori
selection of the control input sampling region is required to determine the
local norm bounds. This leads to a "chicken and egg" problem, where the local
norm bounds are required for controller synthesis, but the region of control
inputs needed to be characterized cannot be known prior to synthesis of the
controller. To tackle this issue, we constrain the closed-loop control inputs
within the sampling region while synthesizing the controller. As the resulting
synthesis problem is non-convex, three semi-definite programs (SDPs) are
obtained through convex relaxations of the main problem, and an iterative
algorithm is constructed using these SDPs for control synthesis. Two numerical
examples are included to demonstrate the effectiveness of the proposed
algorithm.
