Pole assignment with eigenvalue and stability robustness

This paper presents a computation method for pole assignment with eigenvalu e and stability robustness. The robustness measure is constructed to balanc e the tradeoff between an eigenvalue sensitivity measure and a stability ro bustness measure, both defined in terms of the non-differentiable spectral norm. It is established that the robustness measure can be minimized asympt otically via a sequence of smooth unconstrained minimizations involving som e auxiliary objective functions. Moreover, the sequence of minimizers conve rges to the set of minimizers of the robustness measure. A numerical algori thm with analytical formulae of the gradient of the auxiliary objective fun ctions is provided. Through a numerical example and comparing with other me thods, the idea of using a combined robustness measure in the design is ill ustrated and the effectiveness of the computation is demonstrated.