Stability of switched positive systems with unstable subsystems

The stability problem of switched positive systems (SPSs) with unstable subsystems is studied. Two kinds of SPSs are studied, of which the subsystems are partially unstable and all unstable. For stability analysis, a delicate time-scale multivariate linear copositive Lyapunov function (TSMLCLF) is established. The constructed Lyapunov function changes with time in some designed time intervals, and is time-invariant outside these time intervals. Fast and slow mode-dependent average dwell time (MDADT) techniques are used to solve stability problem with unstable and stable subsystems, respectively. Moreover, some improved conditions to ensure the stability of the system are proposed. Finally, two examples are given to verify the effectiveness of our presented method.