This study proposes the two types of bumpless control schemes with disturbance suppression \(L_1\) -gain performance for switched positive linear systems, respectively, utilizing a clock-dependent copositive Lyapunov function and a convex copositive Lyapunov function under restrictive state-dependent switching. In order to mitigate both input and rate bumps caused by switchings, a definition of dual anti-bump switching control performance is introduced based on 1-norm. The clock-dependent copositive Lyapunov function is built by positive vector-valued functions, with sum-of-squares approximation employed to solve the vector-valued functions in the proposed sufficient condition. On the other hand, the convex copositive Lyapunov function is established by constructing first-order convex functions, and its sufficient condition is solved using linear programming technique. Copositive Lyapunov function, switching signal and time-varying controller are co-designed to achieve multiple control objectives, including positivity, disturbance suppression performance, and dual anti-bump switching performance. A series of comparative studies on a turbofan engine model show that the dual anti-bump switching control scheme proposed in this paper outperforms other bumpy or bumpless transfer techniques, but such superiority comes at the cost of higher computational complexity.
