Abstract: An integral invariance principle is extended to discuss the stability of switched linear systems. The integral invariance principle proposed in this paper can be viewed as an extension of the LaSalle invariance principle. The convergence of the solutions to a set in which the system outputs are zero is obtained by using the integrability of the system outputs instead of the Lyapunov function. Moreover, the relationship between the stability of the state set and the switching signals is discussed. Asymptotic stability of the equilibrium can be obtained under the condition that the switched linear systems are observable. Numerical examples are employed to verify the proposed method.