Discrete-time switched linear systems are considered. Extending the notion of connected switched systems earlier proposed for the continuous-time case, the notion of connected discrete switched systems is introduced. For connected discrete switched systems necessary and sufficient existence conditions of a common quadratic Lyapunov function are obtained, that serves a sufficient conditions for stability of that switched systems under arbitrary switching. The set of connected discrete switched systems includes control systems with several sector constrained time-varying nonlinearities considered in the absolute stability theory. The cases of switching among two and among three subsystems are considered in particular. An example is presented.