Spectrum-based stability analysis and stabilisation of systems described by delay differential algebraic equations

An eigenvalue-based framework is developed for the stability analysis and stabilisation of coupled systems with time-delays, which are naturally described by delay differential algebraic equations. The spectral properties of these equations are analysed and a numerical method for computing characteristic roots and stability assessment is presented, thereby taking into account the effect of small delay perturbations on stability. Subsequently, the design of stabilising controllers with a prescribed structure or order is addressed, based on a direct optimisation approach. The effectiveness of the approach is illustrated with numerical examples. All algorithms have been implemented in publicly available software.