Exponential stability of switched positive systems with all modes being unstable.

Summary: This article studies the exponential stability of continuous‐time switched positive systems consisting of unstable subsystems. Different from the existing results, both stabilizing and destabilizing switching behaviors act in the switching sequences. By employing multiple composite copositive Lyapunov functions, sufficient condition is derived to ensure the exponential stability of the system, which evaluates the ratio of stabilizing switching behaviors to compensate the state divergence caused by either unstable subsystems or destabilizing switching behaviors. Simulations demonstrate the effectiveness of the result. [ABSTRACT FROM AUTHOR]