Abstract: A class of multivariable linear system with coupling effect, matched uncertainty and time-varying interference was investigated, for which a new improved <i<L</i<<sub<1</sub< adaptive control was proposed. Firstly, the linear decoupling control was developed for problem of coupling effect. Compared to traditional decoupling control whose closed-loop system was in a critical stable state, the proposed decoupling control guarantees both decoupling and stability. Secondly, after decoupling control, the controlled system can be divided into several decoupled subsystems with matched uncertainty and time-varying disturbances.<i<L</i<<sub<1</sub< adaptive control was then utilized to cope with the uncertainty and interference, which actually ensures robustness of closed-loop system. Moreover, step signal or square-wave signal will be replaced with a differentiable signal to avoid the extremely large transient amplitude or oscillation of control input. Finally, the attitude control problem was addressed with the proposed control law, and simulation results indicate that the improved <i<L</i<<sub<1</sub< adaptive control is effective and efficient.