This paper addresses analysis and switching control problems of switched linear systems. To this end, a mixed time-driven and state-dependent switching strategy is proposed. It guarantees an average dwell time even when all subsystems are unstable. The switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and satisfy a weighted L2 gain performance. The proposed analysis and switching control approach could refrain frequent switches commonly observed in min-switching based designs. The effectiveness of the proposed approach has been illustrated through a spherical inverted pendulum example. © 2014 Elsevier B.V. All rights reserved.