Super-twisting-like algorithm in discrete time nonlinear systems

A new discrete time super-twisting-like second order sliding mode algorithm (DSTA) is proposed. The stability proof of the suggested scheme is analyzed in terms of the discrete Lyapunov approach and Linear Matrix Inequalities (LMI) theory. Using these two tools it is proved that, system state trajectory is ultimately bounded in finite time. The state estimation problem for a class of second order discrete time system has been proposed to show the positive settings obtained from the algorithm introduced here. Also, the ultimate boundedness of the estimation error is demonstrated despite the presence of bounded perturbations. Simulation results illustrates the efficacy of this new discrete-time algorithm.