Abstract: Stability problem of a class of switched linear systems is studied,of which the subsystem matrices are in diagonal canonical or Jordan canonical forms.Monotonicity of the system energy function(the 2-norm of state vector) is analyzed with the solutions of state equation.Sufficient conditions of the asymptotical stability in any switching sequence are obtained for this class of systems.Furthermore,the switching sequence,which makes the switched linear systems asymptotically stable,can be designed easily with these conditions.A numerical example is provided to illustrate the effectiveness of the obtained results.