Direct adaptive control designs for nonlinear discrete-time systems with matched uncertainties

In this paper, we developed a direct adaptive control framework for MIMO nonlinear uncertain systems with matched exogenous disturbances, which are confined to admissible classes and characterized unmodeled dynamics and uncertain nonlinearities. We emphasize that the frameworks are Lyapunov-based and the proposed controllers address adaptive stabilization. Furthermore, A factored adaptive gain matrices are obtained when extended to linear systems. Finally, the proposed framework is applied to a numerical example for demonstration.