Robust Stability of a Class of Interconnected Nonlinear Positive Systems

Abstract—We present conditions for robust stability of a class of linear systems interconnected by uncertain nonlinear, norm-bounded functions. We show that such conditions can be reformulated as classical small gain like conditions for a related linear system. Under further assumptions that render the related linear system positive, we show that we can achieve sharp tractable conditions for robust stability of the original nonlinear system. I