The state transfer of closed quantum systems in the interaction picture is studied. The convergent problem encountered in designing control laws based on the Lyapunov method is solved by the well constructed observable operator and a path programming control strategy. It is proved that the condition for the target state being a stable point in the Lyapunov's sense is the coherent vectors of the observable operator and the target state must be in opposite directions. For the local optimisation limitation of the Lyapunov-based method, the path programming control strategy is proposed, which is used to change the distribution of stationary points or choose a transition path by appropriately selecting intermediate target states. Comparative numerical system simulation experiments are implemented on a four-level quantum system and the experimental results are analysed.

The authors deal with mode and parameter-dependent robust mixed ℋ₂/ℋ_∞ filtering design for a class of discrete-time switched polytopic linear systems. The objective is to design a homogeneous switched mixed ℋ₂/ℋ_∞ filter guaranteeing the asymptotic stability of the resulting filtering error systems with given performance measures. Based on a switched parameter-dependent Lyapunov function combined with Finsler's lemma, some novel conditions for robust ℋ₂ and ℋ_∞ performance analysis are proposed and in turn the filter synthesis is developed. It is shown that by using a new linearisation technique combined with a bounding approach, the filter gains can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.