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