On the role of reachability and observability in NMR experimentation
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It is shown that the system theoretic concepts of reachability and observability are relevant to the analysis of NMR experiments. Moreover, the sets of reachable states are examined and Lie theoretic criteria are given for the reachability of the system. The question is investigated how the set of reachable states depends on the class of input functions that are allowed. Both one‐dimensional and multi‐dimensional NMR experiments are considered.
KeywordsInput Function Free Induction Decay Reachable State Bilinear System Path Planning Problem
- R.R. Ernst, G. Bodenhausen and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, 1987).Google Scholar
- K. Grasse and H.J. Sussmann, Global controllability by nice controls, in: Nonlinear Controllability and Optimal Control, ed. H. Sussmann (Dekker, 1990) pp. 33–79.Google Scholar
- A. Isidori, Nonlinear Control Systems, 3rd ed. (Springer, 1995).Google Scholar
- V. Jurdjevic, Geometric Control Theory (Cambridge University Press, 1997).Google Scholar