Minimum Ultimate Band Design of Discrete Sliding Mode Control

The paper presents a generalized understanding on the dynamics of the sliding variable for discrete time sliding mode control systems via a fresh approach involving several bands in the space of the sliding variable. Using this analysis, controller parameters can be obtained once the ultimate band is chosen. It is shown that on choosing the least ultimate band, the control becomes non-switching and Gao's reaching law becomes identical to Utkin's reaching law. On other occasions, the ultimate band obtained using this approach is clearly less than that obtained in previous works using Gao's reaching law. The analysis is presented for both state feedback and multirate output feedback cases