Stability analysis of equilibrium positions of mechanical systems with delay via decomposition

A nonlinear mechanical system with time delay is studied. It is assumed that the system is influenced by linear velocity forces and nonlinear nonhomogeneous positional forces. Moreover, the case is considered when there exists a delay in the positional forces. On the basis of the decomposition method, conditions are derived under which the trivial equilibrium position of the investigated system is asymptotically stable for an arbitrary continuous nonnegative and bounded delay.