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International audienceWe analyze the energy-minimizing  problem for a two-level dissipative quantum system described by the Kossakowsky-Lindblad equation. According to the Pontryagin Maximum Principle (PMP), minimizers   can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous  analysis  concerning  2D  solutions in the case where the Hamiltonian dynamics are integrable

Energy Minimization Problem in Two-Level Dissipative Quantum Control: Meridian Case