This paper introduces a mathematical formula for calculating the eigenvalue differential sensitivities of the closed-loop state matrix with respect to a disturbance matrix when the closed-loop system is subjected to an additive structured perturbation. The robust pole assignment problem is then formulated as an optimization task in which the differential sensitivities of the closed-loop poles are minimized. The case of “multi-perturbations” can be considered naturally in our problem formulation. The gradient of the objective function to be minimized is then derived which permits the minimization to be proceeded effectively. Numerical examples are then employed to illustrate the design technique.
An Optimal Differential Sensitivity Approach to Pole Assignment for Structurally Perturbed Systems
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Tam, H. K., and Lam, J. (September 1, 1999). "An Optimal Differential Sensitivity Approach to Pole Assignment for Structurally Perturbed Systems." ASME. J. Dyn. Sys., Meas., Control. September 1999; 121(3): 410–417. https://doi.org/10.1115/1.2802489
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