Abstract
In this paper, we investigate the state convergence problem for closed quantum systems under degenerate cases. An implicit Lyapunov-based control strategy is proposed for the convergence analysis of finite dimensional bilinear Schrodinger equations. The degenerate cases that the systems do not satisfy the strong regular condition [17] and the condition 〈φ i |H 1 |φ j 〉 ≠= 0, i, j ≠= k for eigenstates φ i , φ j of H 0 different from target state φ k , are considered. First the Lyapunov function is defined by the implicit function and the existence is guaranteed by a fixed point theorem. Then the convergence analysis is investigated by the LaSalle invariance principle. Finally, an example is provided to show the effectiveness of proposed results.
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