The problem of ultimate bound for the switched linear systems is studied. Firstly, the componentwise ultimate
bound for the switched linear systems is obtained by using both the minimum dwell time method and the componentwise
ultimate bound method. Then, a novel method which can estimate the minimum dwell time for such switched systems
is proposed based on the 2-norm method. In the comparison with the previous methods, the obtained method has some
advantages over those in some cases, which reduces the conservative property of the estimation. Finally, a numerical
simulation results show the correctness and effectiveness of the obtained results.