Abstract
The asymptotic stability and instability of the trivial solution of a functional-differential equation of delay type relative to part of the variables are investigated using limit equations and a Lyapunov function whose derivative is sign-definite. The theorems thus obtained are used to solve the problem of stabilizing mechanical control systems with delayed feedback. As examples, solutions of problems of the uniaxial and triaxial stabilization of the rotational motion of a rigid body with a delay in the control system are presented.
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