Stability analysis of nonstationary mechanical systems with time delay via averaging method

A linear mechanical system with constant matrix of dissipative forces and continuous bounded matrices positional is studied. It assumed that there are a large positive multiplier at the vector delay in forces. The case considered where associated delay-free averaged asymptotically stable. With aid Lyapunov direct method averaging method, conditions derived under which neither nor timevarying perturbations zero mean values disturb asymptotic stability. developed approach used problem monoaxial stabilization rigid body.