This paper investigates robust stability and \(L_2\) -gain analysis for switched systems subject to actuator saturation and parameter uncertainty. An admissible chain-dependent average dwell time strategy formed by integrating consecutive admissible transfer edges into transition chains is adopted to regulate the dynamic switching behavior of each subsystem, thereby mitigating the inherent conservatism in the traditional dwell time. Moreover, a convex hull representation is employed to address the saturation behavior of actuators, and the asynchronous switching behavior between subsystems and controllers is simultaneously considered. An admissible edge-based Lyapunov function is constructed to weaken the adverse effects induced by asynchronous switching. Accordingly, an edge-dependent controller is proposed, and sufficient conditions are derived to ensure robust asymptotic stability for uncertain systems with \(L_2\) performance. Finally, numerical simulations demonstrate the effectiveness of the proposed approach.
