In this project we use the second method of Lyapunov to develop several controllers to stabilize discrete-time dynamical systems with or without parameter uncertainties and/or external disturbances. We also use the notion of a sliding mode on a preferred hyperplane, previously developed for continuous-time variable structure control systems, to stabilize discrete- time dynamical systems. In particular, feedback controllers are proposed that: (i) stabilize discrete systems with no uncertainties by forcing their state trajectories onto prespecified hyperplanes; (ii) provide a needed level of stability robustness to discrete systems with uncertainties which are modeled by cone bounded functions; (iii) robustly stabilize discrete uncertain systems.

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