On the existence of a common Lyapunov function for a family of nonlinear positive systems

Abstract This paper is devoted to the stability analysis of a class of switched nonlinear positive systems with nonlinearities of a sector type. A special construction of common Lyapunov function is proposed for the family of subsystems associated with a switched system and conditions of the existence of such a function are derived. The obtained results are used for the absolute stability investigation of switched systems with rank one difference.