Abstract
An eigenvalue based framework is developed for the stability analysis and stabilization of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations are analyzed and a numerical method for stability assessment is presented, taking into account the effect of small delay perturbations on stability. Subsequently, the design of stabilizing controllers with a pre-scribed structure or order is addressed, based on a direct optimization approach. The effectiveness of the approach is illustrated with numerical examples, and the similarities with the computation and optimization of ℋ∞ norms are pointed out.
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