Sliding mode control for discrete time-delay nonlinear systems with uncertainty and packet loss

The sliding mode control (SMC) problem is investigated for a discrete time-delay nonlinear systems with uncertainties and packet losses. The uncertainties may occur randomly and be assumed to be norm-bounded. The delays are time-varying but bounded functions. Firstly, under the assumption that the dropout probability is known, the states of the system are constructed, and the sliding mode function with dropout probability is designed. By using the Lyapunov method, the asymptotic stability of the sliding motion is proved. Secondly, the sliding mode control is designed by using GAO´s reaching law, the reachability of sliding mode surface is also proved. Finally, a numerical example is constructed to illustrate the effectiveness of the results obtained.