Exponential stability of switched positive systems with homogeneous degree less than one

This paper investigates the stability of positive switched homogeneous systems (PSHSs) with exogenous inputs. The purpose of the article is to propose a sufficient condition for global exponential stability (GES) of PSHSs by using the novel inequality and comparison principle. Compared with the traditional Lyapunov function method, our approach is more concise, intuitive, and widely applicable. At first, we provide a new inequality that will be used for stability analysis of the system. Then, combining the new inequality and a rigorous proof by contradiction, we establish the stability criterion based on the slow switching technique, and the obtained result is extended to a general degree of α in the range of 0 to 1, deepening and developing some previous research findings. Finally, the article further demonstrates the effectiveness of the theoretical discoveries through an important example.