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Novel Power-Rate Reaching Law for Quasi-Sliding Mode Control

This study elaborates on the quasi-sliding mode control design for discrete time dynamical systems subject to matched external disturbances and modeling uncertainties. In order to provide finite time convergence to the sliding surface and at the same time restrict the control effort, we propose a novel power-rate reaching law utilizing a hyperbolic tangent function. The construction of the reaching law ensures that when the distance between the representative point of the system and the sliding surface is significant then the convergence pace is limited, which results in a reduced control effort. However, as the representative point of the system approaches the sliding surface, the convergence pace increases. Moreover, the study adopts a non-switching-type definition of the sliding motion, which eliminates undesirable chattering effects in the sliding phase. In order to reduce the impact of external disturbances on the system, the model following approach is taken, which allows for the rejection of all but the last disturbance value.