A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination

This paper addresses the state-feedback stabilization problem for a class of high-order uncertain nonlinear systems with multiple time-delays. The distinguished feature of the systems to be investigated is the serious coexistence between unknown time-varying parameters and unknown multiple time-delays. Time-varying method combined with adaptive technique is used to capture the possible unknowns and delayed states. The new control strategy is presented based on homogeneous domination idea and the choice of a Lyapunov–Krasovskii functional. Finally, the developed scheme is used to stabilize mass-spring mechanical system with unknown time-delays.