An LMI Approach for the Stabilization of Discrete-Time Delay Nonlinear Systems Using Backstepping

In this paper, an-LMI approach is utilized for the stabilization of Discrete-Time Delay Nonlinear Systems (DTDNS). The delay provided is state-delay. The control criterion is derived in terms of linear matrix inequalities (LMI's). The controller is designed by making use of back stepping technique. By choosing an appropriate Lyapunov function, some mathematical manipulations have been carried out to deduce simple LMI condition for asymptotic stabilization. The effectiveness and the applicability of the proposed control law is verified through simulation.