Stability analysis of mechanical systems with distributed delay via decomposition

The article analyzes a linear mechanical system with large parameter at the vector of velocity forces and distributed delay in positional forces. With aid decomposition method, conditions are obtained under which problem stability analysis original second-order differential equations can be reduced to studying two auxiliary first-order subsystems. It should noted that one subsystems does not contain delay, whereas for second subsystem containing formulated terms feasibility systems matrix inequalities. To substantiate this decomposition, Lyapunov direct method is used. Special constructions Lyapunov—Krasovskii functionals proposed. developed approach applied monoaxial stabilization rigid body. results numerical simulation presented confirming conclusions analytically.