On the stabilization of bilinear systems via constant feedback

We study the problem of stabilization of a bilinear system via a constant feedback. The question reduces to an eigenvalue problem on the pencil A+α0B of two matrices. Using the idea of simultaneous triangularization of the matrices involved, some easily checkable conditions for the solvability of this question are obtained. Algorithms for checking these conditions are given and illustrated by a few examples

Feedback control of spin systems

The feedback stabilization problem for ensembles of coupled spin 1/2 systems is discussed from a control theoretic perspective. The noninvasive nature of the bulk measurement allows for a fully unitary and deterministic closed loop. The Lyapunov-based feedback design presented does not require spins that are selectively addressable. With this method, it is possible to obtain control inputs also for difficult tasks, like suppressing undesired couplings in identical spin systems.Comment: 16 pages, 15 figure