On the existence of linear copositive Lyapunov functions for 3-dimensional switched positive linear systems

This paper is focused on deriving easily verifiable conditions for the existence of common linear copositive Lyapunov functions for 3-dimensional switched positive linear systems. Unlike some results in the literature, the existence of a common linear copositive Lyapunov function is only determined by two constants given in terms of the entries of system matrices. The structure of all common linear copositive Lyapunov functions is characterized clearly. We also extend the main result to the discrete case and the case of control input.