This article is devoted to the output-feedback H∞ control problem for switched linear systems subject to actuator saturation. We consider both continuous-and discrete-time switched systems. Using the minimal switching rule, nonlinear output feedbacks expressed in the form of quasi-linear parameter varying system are designed to satisfy a pre-specified disturbance attenuation level defined by the regional 2H∞ (2H∞)-gains over a class of energy-bounded disturbances. The conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation. A spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach. © 2012 Taylor & Francis Group, LLC.