Reachable set estimation for switched positive systems with mixed time-varying delays and bounded disturbances

In this study, the problem of reachable set estimation of switched positive systems with discrete and distributed delays subject to bounded disturbances is studied. The authors first investigate the reachable set of unswitched positive systems. Then, applying a new approach which is different from the Lyapunov functional method, they give a sufficient condition for the existence of a ball such that all the solutions of the switched positive system converge exponentially within it under certain switching rules. In addition, a precise estimation of the decay rate is also presented. Finally, the effectiveness of the theoretical result is illustrated by a numerical example.