Pole assignment with eigenvalue and stability robustness

Abstract

This paper presents a computation method for pole assignment with eigenvalue and stability robustness. The robustness measure is constructed to balance the tradeoff between an eigenvalue sensitivity measure and a stability robustness measure, both defined in terms of the non-differentiable spectral norm. It is established that the robustness measure can be minimized asymptotically via a sequence of smooth unconstrained minimizations involving some auxiliary objective functions. Moreover, the sequence of minimizers converges to the set of minimizers of the robustness measure. A numerical algorithm with analytical formulae of the gradient of the auxiliary objective functions is provided. Through a numerical example and comparing with other methods, the idea of using a combined robustness measure in the design is illustrated and the effectiveness of the computation is demonstrated.