<p>This paper addresses the bumpless transfer control problem for a class of uncertain switched linear systems with parametric uncertainties. A novel adaptive control framework is proposed to achieve asymptotic tracking of a reference switched system while suppressing control chattering during mode transitions. By integrating adaptive laws with slope constraints on parameter adaptation rates, the control strategy ensures both global asymptotic stability and bumpless switching performance. Key contributions include: 1) a dual-layer control architecture combining parameter adaptation and switching dynamics regulation, resolving the traditional trade-off between stability and transient performance in switched systems; 2) a time-varying piecewise Lyapunov function approach with dwell-time constraints, establishing stability criteria through dynamic coupling analysis of adaptive laws and switching signals; 3) a practical verification platform using aero-engine multi-mode models.</p>