L∞-gain analysis for positive systems with distributed delays

This paper addresses the L∞-gain analysis problem of positive linear systems with distributed delays. By virtue of the positivity and linearity of the system, we first study the monotonic and asymptotic property of the system with distributed delays. Then, by resorting to an auxiliary system without time delay, an explicit expression of the L∞-gain of positive systems with distributed delays is given in terms of system matrices. Moreover, the results are extended to positive systems with distributed delays over a bounded time-varying interval. Finally, a necessary and sufficient condition on the L∞-gain of an asymptotically stable positive system with distributed delays is presented via linear programming.