Stability of Switched Positive Homogeneous Systems With All Modes Being Unstable

For the first time, this paper investigates the practical stability of switched positive homogeneous systems (SPHSs) where all modes are unstable. Sufficient conditions for the practical stability of SPHSs under external disturbances are established in both continuous‐time and discrete‐time domains. In contrast to previous studies, the stability of SPHSs is based on the framework of convex constraint vector fields. Subsequently, we employ a discretized max‐separable Lyapunov function, in conjunction with an interval dwell‐time (IDT) switching strategy, to analyze the stability properties of the systems under consideration. Since these convex constraints are inherent to linear systems, the derived results can naturally be applied to switched positive linear systems (SPLSs). Finally, the theoretical results are confirmed through two numerical examples.