Row and Column Representatives in Qualitative Analysis of Arbitrary Switching Positive Systems

Consider an arbitrary switching positive system whose (discrete- or continuous-time) dynamics is defined by the matrix se tA. The class of copositive Lyapunov functions called "polyhedral" is charact erized by necessary and sufficient conditions derived from the solvability of some inequalities built with the matrices in A, and from the properties of the row representatives of A. Duality is proven between the "polyhed ral" class and the already known class of "linear" copositive Lyapunov functions (characterized by equivalent conditions derived from the propert ies of the column representatives of A). A numerical example illustrates the utilization of two types of approaches, as well as the connection among them.