Eigenvalue based analysis and controller synthesis for systems described by delay differential algebraic equations

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.