Positive switched systems have attracted increasing attention from researchers. This paper addresses the existence problem of common linear copositive Lyapunov function for positive linear switched systems, both discrete- and continuous-time cases are considered. If the system matrices of two linear systems are mutually transposed, then these two systems are said to be mutually dual, or one is the duality of the other one. This paper proposes some simple necessary and sufficient conditions which can determine whether or not two-dimensional dualsystems (continuous- or discrete-time) simultaneously possess corresponding common linear copositive Lyapunov function. A numerical example is provided to demonstrate the theoretical results.

positive switched linear system, dual systems, switching signals, stability, linear programming.