Reachable set estimation for positive linear discrete-time systems under the constrained disturbance

This paper studies the problem of estimating the reachable set boundary of positive discrete-time systems with specific inputs in hyperspace. When the L1-norm or L infinity-norm of the particular disturbance input to a positive linear discrete-time system is bounded by a constant, by using linear copositive Lyapunov functional method based on S-lemma, the reachable set could be constrained in a hyper-pyramid under some matrix inequality conditions. In an innovative way, by the method of directly calculating the dynamic trajectories of the system state, the reachable set can also be constrained in a hyper-rectangle. The approach of shrinking the size of the reachable set region is also developed. Finally, the validity of the results obtained is verified by examples of passenger flow in and out of customs.