Robust pole assignment in high-order descriptor linear systems via proportional plus derivative state feedback

The problem of robust pole assignment (RPA) in high-order descriptor linear system is considered. By using the result of eigenstructure assignment via proportional plus derivative state feedback and the perturbation theory of generalised pole problem proposed by Stewart, the RPA problem in high-order descriptor linear system is converted into a minimisation problem, and a simple algorithm is derived for solution to this RPA problem. An example of third-order is worked out with multiple solutions, both the indices and the numerical robustness test demonstrate the effect of the proposed approach.