Lessons from an example in “On the stability of discrete-time sliding mode control systems”

Initial conditions are presented for which the indicated example in the above paper by Sarpturk et al. (ibid. vol.AC-32 (1987)) is shown to fail to meet the paper´s theoretical requirements. The importance of this error is that the example now represents a counterexample to the suggested form of the sliding mode control, demonstrates a necessary restriction on any such quasi-sliding mode control, and illustrates that restrictions presented in another paper are not global