This work investigates the \(H_{\infty }\) output tracking bumpless transfer control (HOTBTC) problem of switched linear systems under asynchronous switching. By virtue of the gain interpolation technique, a bumpless transfer (BT) controller which can generate a continuous control input is designed. Then, the notion of the HOTBTC problem for the considered system is presented. Based on multiple Lyapunov functions, a criterion to ensure the solvability of the HOTBTC problem is established. Finally, a turbofan model is taken as an example to reveal the validity of the presented results. In contrast to the existing results, the typical advantages of this work are twofold: (a) The dwell time of sub-modes is allowed to be less than the upper bound of the switching delay. (b) There is no requirement that the expected running time of the gain interpolation is less than the dwell time of sub-modes.
