Reconstructing Sliding Surfaces for SISO Variable Structure Output Feedback Control Systems Using Inverse Method

There exists a dynamic mapping relationship between the sliding variable and the output variable in a linear, time-invariant (LTI), single-input-single-output (SISO) system. This relationship is invariant of the matched disturbances, which lies in the control space. In this note, a continuous-time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output. This inverse compensator is stable and causal provided that the original SISO system is minimum phase and that the input-output relative degree is less than or equal to one. In case the system relative degree is greater than one, a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete-time to the accuracy of O(T), where T is the sampling period. Thus the discrete-time variable structure control (VSC) law can be implemented without full state accessibility.