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This paper is devoted to a stabilization problem for a servo-system under the influence of friction. The proposed approach is based on a multi-objective control design using a reduced-order velocity observer, a generalized Maxwell-slip (GMS) model-based friction compensation and a linear time invariant (LTI) compensator simultaneously. Stabilization conditions on interconnected systems are investigated with strictly positive real (SPR) condition on linear closed-loop dynamics of hierarchical systems using linear matrix inequality (LMI) frameworks. The appeal of this proven theoretical design is further demonstrated by numerical results.