Notes on sliding mode control of two-level quantum systems

In [Dong, D. and Petersen, I.R. (2012). Sliding mode control of two-level quantum systems. Automatica, 48, 725-735], a sliding mode control approach has been proposed for two-level quantum systems to deal with bounded uncertainties in the system Hamiltonian. This paper further extends these results in two directions. One extension is to consider the effect of uncertainties during the process of driving the system's state back to the sliding mode domain from outside and we propose two approaches to accomplish this control task. The other extension generalizes the previous design approach to consider uncertainties described as perturbations in the free Hamiltonian.