OPTIMAL GYROSCOPIC STABILIZATION OF VIBRATIONAL SYSTEM: ALGEBRAIC APPROACH

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.