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The stabilization of unstable nonlinear systems and tracking control arechallenging engineering problems due to the encompassed nonlinearities indynamic systems and their scale. In the past decades, numerous observer-basedcontrol designs for dynamic systems in which the nonlinearity belongs toLipschitz functions have been proposed. However, most of them only focus onoutput feedback and consequently, state feedback design remains less developed.To that end, this paper is dedicated to the problem of full-state feedbackcontroller design for discrete-time Lipschitz nonlinear systems. In addition,we present a simple iterative method for improving the convergence of theclosed-loop performance. It is later demonstrated that our approach can beconveniently extended and utilized for output tracking.

Feedback Stabilization and Output Tracking for Discrete-Time Lipschitz Nonlinear Systems via Iterative Convex Approximations