Soft sliding mode controller design for uncertain delta operator systems

Aiming at high-speed signal sampling system with internal parameter perturbation and external disturbance, a novel delta operator saturated variable rate reaching law based on sigmoid function is presented, and soft sliding mode controller design is addressed for delta operator systems with uncertainties in the paper. The structural feature of uncertain delta operator system is concerned. Soft sliding mode controller design for continuous-time system and discrete-time system can be converted to the case of delta operator system. The stability of uncertain delta operator soft sliding mode control (SMC) system is guaranteed by Lyapunov stability theory. Soft sliding mode controller design for uncertain delta operator systems is achieved by the proposed reaching law under a certain matching condition. It is illustrated that delta operator soft SMC system by the proposed reaching law in a simulation example can not only reach the scope of the switching plane in limited time, but also reduce system chattering effectively. The system on stability and process steady is better than that of delta operator exponential reaching law and delta operator variable rate reaching law. At the same time, the system has a good completely robustness compared with delta operator statured reaching law.