Post-filtering approach to output feedback variable structure control for single-input-single-output sampled-data systems

This study presents a dynamic post-filtering approach to a single-input-single-output sampled-data variable structure output feedback control problem. Given a sliding surface, Sigma(x)=0 (x being the system state vector), designed through standard procedures with the assumption of full state accessibility, a dynamic filter, denoted post-filter, is employed to synthesise Sigma(x) by means of output variable alone. In contrast with a state observer, the post-filter is invariant of the matched disturbances; and it requires only partial information of the system parameters. Thus, the robustness property of the variable structure system is retained. Let T be the sampling period. A sampled-data realisation of the post-filter is done by zero-order hold. Depending on the system relative degree, either Sigma_k or Sigma_k-1 can be obtained for implementing the variable structure control law. A discrete-time switching-type control law, which is originally designed to satisfy the continuous-time reaching condition, will lead to a quasi-sliding motion, forming a boundary layer of thickness O(T) about the sliding surface. The stability of the post-filter is ensured if the system output is in minimum phase and that the sliding mode dynamics are chosen properly.