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Abstract Mitigation of space debris draws much concern today since its steadily increasing number and the consequent increased risk of space activities. Among all the active debris removal strategies, tethered space-tug is considered as a promising method due to its safeness of capture and dynamic stability of pull strategy. Although promising, challenges remain in its position and attitude control especially when the target is tumbling, which may cause damage to the appendages or result in collisions. This paper addresses the problem of position and attitude control of a tethered space-tug system with only tether tension available for the target. Based on Takagi-Sugeno fuzzy technology, a guaranteed cost guidance and control law is obtained by solving a set of linear matrix inequalities. The effectiveness of the guidance and control strategy is validated by numerical simulations. [ABSTRACT FROM AUTHOR]