Geodesic
Optimal gyroscopic stabilization of vibrational system: algebraic approach
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 70-80

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The paper deals with LTI vibrational systems with positive definite stiffness matrix $K$ and symmetric damping matrix $D$. Gyroscopic stabilization means the existence of gyroscopic forces with a skew-symmetric matrix $G$, such that a closed loop system with damping matrix $D+G$ is asymptotically stable. The feature of characteristic polynomial in the case predetermines such stabilization as a low order control design. Assuming the necessary condition of gyroscopic stabilization is fulfilled, we pose the problem of achieving relative stability maximum using a stabilizer $G$. The stability maximum value is determined by a matrix $D$ trace, but its reachability depends on the coincidence of all pole real parts with the corresponding minimal value, i.e. equality of characteristic and root polynomials. We illustrate a root polynomial technique application to optimal gyroscopic stabilizer design by examples of dimension 3–5.
Keywords: vibrational system, gyroscopic stabilizer, low order control, rightmost poles, relative stability, root polynomial. 
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     author = {A. V. Chekhonadskikh},
     title = {Optimal gyroscopic stabilization of vibrational system: algebraic approach},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {70--80},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a23/}
}
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A. V. Chekhonadskikh. Optimal gyroscopic stabilization of vibrational system: algebraic approach. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 70-80. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a23/