State feedback stabilization of discrete-time nonlinear systems

In this note, we investigate the problem of state feedback stabilization of affine nonlinear discrete-time systems. From a prescribed Lyapunov function and a modified Riccati equation, we show that the proposed state feedback law covers a large class of dynamical systems. In particular when the unforced dynamic model is not Lyapunov stable. Sufficient conditions for asymptotic stabilization are expressed in terms of matrix inequalities. High performances of the proposed technique will be shown through academic examples.