A new method for constructing sliding surfaces of linear time-invariant systems

A new method for constructing the sliding surfaces is developed by using the pole-assignment method; unlike the usual cases, the pole-assignment method is applied to the overall closed-loop system and not the system in the sliding mode. Most importantly, the design procedure is simple since the sliding surfaces can be determined in an explicit form. Also, three significant properties listed in a theorem are proved and demonstrated by a numerical example.