We consider finite-dimensional Markovian open quantum systems, and characterize the extent to which time-in- dependent Hamiltonian control may allow to stabilize a target quantum state or subspace and optimize the resulting convergence speed. For a generic Lindblad master equation, we introduce a dissipation-induced decomposition of the associated Hilbert space, and show how it serves both as a tool to analyze global stability properties for given control resources and as the starting point to synthesize controls that ensure rapid convergence. The resulting design principles are illustrated in realistic Markovian control settings motivated by quantum information processing, including quantum-optical systems and nitrogen-vacancy centers in diamond

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Summary This paper considers the problem of optimizing the operation of Indirect Adiabatic Cooling (IAC) systems with application to data centers. Optimal operation is achieved when the required cooling demand is satisfied at the minimum energy cost. For this purpose, we design a supervisory control system, where the higher layer determines the optimal set‐points for the local controllers by employing an Extremum Seeking Control (ESC) scheme. In particular, we consider a Newton‐like phasor ESC, which augments the derivative estimator underlying the phasor approach to capture also the Hessian of the plant index and then it uses these estimates to steer the system along a Newton‐like direction. The effectiveness of the considered approach is tested in simulation by exploiting a Matlab‐based simulation environment including an IAC system and a computer room.