Robust stability optimisation of DDAE of retarded type

Minimization of the mean of the spectral abscissa with Variance penalty for DDAEs

The approach is concerned with an eigenvalue based stabilization method for uncertain linear time-delay systems by static or dynamic feedback, where the closed-loop systems is described by a delay-differential algebraic equation (DDAE) of retarded type. Both system matrices and delays can be subject to uncertainty, modeled by a random vector. The dependence of the characteristic matrix on the uncertain parameters can be nonlinear.
Unlike the stability optimization methods for deterministic problems, which minimizes the spectral abscissa, this approach shows better robust properties based on a more realistic model, where the uncertainty is taken into account by minimizing an objective function, consisting of the mean of the spectral abscissa with a variance penalty.
The minimization of the objective function requires the usage of the software HANSO (Hybrid Algorithm for Non Smooth Optimization). In order to numerically evaluate the objective function, a grid obtained with Quasi Monte Carlo methods is fixed. For every point of the grid, the spectral abscissa is evaluated by the Infinitesimal Generator Approch, this approximation is corrected by applying Newton's method to the characteristic equation.

REFERENCE: http://www.cs.kuleuven.be/publicaties/rapporten/tw/TW671.pdf