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This note studies the asymptotic stability of switched positive linear discrete systems whose subsystems are (sp) matrices. Such a matrix is the character of a kind of asymptotically stable linear systems and it is very easy to test. A new definition of (sp) matrix is given by means of graph theory. Based on an approaching using partially ordered semigroups and Lie algebras, we present several new criteria for asymptotic stability. We also derive an algebraic condition and discuss a kind of higher order difference equation. Our results have a robustness property to some extent.