Sliding Mode Control For Discrete Time-delay Uncertainty Systems With Packet Loss

The sliding mode control problem is investigated for a class of discreteuncertain systems with time-delay and packet losses. Random uncertainties, extenraldisturbance and packet losses as inevitably phenomenon, are otfen encountered inactual systems. Therefore, the sliding mode control problem for the addressedsystems not only has significance in practical system, but also has a high value due toits good performance.The state estimation method is obtained for the discrete time-delay systemswith input channel uncertainty, random parameter uncertainties and packet loss，alsothe discrete time sliding surface with packet loss probability is constructed. At thesame time，by using Lyapunov method and LMI approach，the condition has beenpresented to guarantee the asymptotical stability of the addressed system，when thesystem reach the ideal sliding mode surface under the equivalent control. Byapplying the reaching law, the sliding mode control law is designed, and theaccessibility of the control law is investigated. It should be noted that, the statetrajectory tend to be on the default sliding mode surface, and will not be affected bydata packet loss and uncertainties. The sliding mode is asymptotically stable on thedefault sliding surface.Motivated by the above discussions，considering the external disturbance andrandom nonlinear uncertainties of the input channel, similar to the process wediscussed, the sliding mode control is designed without external disturbance. Thecondition of sliding mode has been discussed with a specified disturbance level. Thesliding mode control law is designed, and the accessibility of the control law isinvestigated. It should be noted that，the state trajectory tend to be on the defaultsliding mode surface, and will not be affected by external disturbance，data packetloss and input channel uncertainties. The sliding mode is also asymptotically stableon the default sliding surface.Finally, the numerical examples are shown to verity the feasibility and effectiveness of the proposed results.