Exponential Stability of Continuous-Time Switched Delay Positive Systems with All Unstable Modes

In this paper, the stability problem of continuous-time time-varying delay switched positive system (SPS) with unstable modes is studied. Firstly, in the switching sequences, both stabilizing and destabilizing switching behaviors exist, which is different from the existing research content. Secondly, by constructing multiple copositive Lyapunov function, a sufficient condition of exponential stability of the system is given, which can calculate the proportion of the stabilizing switching behaviors in the total switching behaviors, so as to compensate for the state divergence caused by the unstable subsystems or the unstable switching behaviors. Finally, a numerical example is given to verify the validity of the results.