The authors use a singular system setting to provide a geometric theory for dynamical systems under derivative feedback. They define the relevant subspace and provide computational design techniques in terms of a generalized Sylvester or Lyapunov equation for which efficient solution techniques are well-known. The authors provide both geometric and algebraic characterizations of the effects of derivative feedback, drawing connections with previous work in state-variable systems as well as extending that work to singular systems.>
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Lewis et al. (1991) studied this question.
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