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This letter presents a framework for synthesizing a robust full-statefeedback controller for systems with unknown nonlinearities. Our approachcharacterizes input-output behavior of the nonlinearities in terms of localnorm bounds using available sampled data corresponding to a known region aboutan equilibrium point. A challenge in this approach is that if thenonlinearities have explicit dependence on the control inputs, an a prioriselection of the control input sampling region is required to determine thelocal norm bounds. This leads to a "chicken and egg" problem, where the localnorm bounds are required for controller synthesis, but the region of controlinputs needed to be characterized cannot be known prior to synthesis of thecontroller. To tackle this issue, we constrain the closed-loop control inputswithin the sampling region while synthesizing the controller. As the resultingsynthesis problem is non-convex, three semi-definite programs (SDPs) areobtained through convex relaxations of the main problem, and an iterativealgorithm is constructed using these SDPs for control synthesis. Two numericalexamples are included to demonstrate the effectiveness of the proposedalgorithm.

Robust Local Stabilization of Nonlinear Systems with Controller-Dependent Norm Bounds: A Convex Approach with Input-Output Sampling