A global attractivity result for a class of switching discrete-time systems

In this paper we present the global attractivity properties of a class of discrete-time switching systems of the form x(k+ 1) = A_ix(k), A_i epsiv = {A₁,...,A_m}, where each constituent matrices A_i epsiv R^nxn are Schur stable. We assume that a set of non-singular matrices T_ij epsiv R^nxn exist such that the matrices T_ij A_iT_ij ^-1 and T_ij A_jT_ij ^-1 for i, j epsiv {1, ...,m} are upper triangular. We show that for a special subset of such switching systems the origin is globally attractive, and it is possible to prove this without requiring the existence of a common quadratic Lyapunov function (CQLF).