State and output feedback stabilization of a class of discrete-time nonlinear systems

For multi-input multi-output (MIMO) discrete-time nonlinear systems whose free dynamics can be unstable, we show how the problem of global stabilization via state and dynamic output feedback can be solved. Sufficient conditions for stability are deduced, from the Lyapunov approach, and expressed in terms of matrix inequality that depend on arbitrary matrices fixed by the designer. An example is presented to illustrate the high performances of the proposed approach.