This work is devoted to the Keldysh model of flutter suppression and rigorous approaches to its analysis. To solve the stabilization problem in the Keldysh model we use an analog of direct Lyapunov method for differential inclusions. The results obtained here are compared with the results of Keldysh obtained by the method of harmonic balance (describing function method), which is an approximate method for analyzing the existence of periodic solutions. The limitations of the use of describing function method for the study of systems with dry friction and stationary segment are demonstrated.