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

There exists a mapping relationship between the sliding surface variable and the output variable for a linear, time-invariant (LTI), single-input-single-output (SISO) system. This relationship is invariant of the matched disturbances, which lie in the control space. By using the system inversion method, the sliding surface can be reconstructed from the system output. Thus the variable structure control (VSC) law can be implemented without full state accessibility. As will be proved in this paper, the inverse exists if all the system zeros are nonzero and that the sliding surface is properly designed. For SISO systems, both the right inverse and the left inverse can achieve sliding surface reconstruction. Furthermore, if the system is minimum phase, a reduced-order sliding surface (and hence the inverse) will suffice the variable structure output feedback control design.