  This paper deals with the stability analysis problem of discrete-time
switched linear systems with ranged dwell time. A novel concept called
L-switching-cycle is proposed, which contains sequences of multiple activation
cycles satisfying the prescribed ranged dwell time constraint. Based on
L-switching-cycle, two sufficient conditions are proposed to ensure the global
uniform asymptotic stability of discrete-time switched linear systems. It is
noted that two conditions are equivalent in stability analysis with the same
$L$-switching-cycle. These two sufficient conditions can be viewed as
generalizations of the clock-dependent Lyapunov and multiple Lyapunov function
methods, respectively. Furthermore, it has been proven that the proposed
L-switching-cycle can eventually achieve the nonconservativeness in stability
analysis as long as a sufficiently long L-switching-cycle is adopted. A
numerical example is provided to illustrate our theoretical results.
