LAUSR

Abstract This paper investigates the stability and L ∞ -gain problems of positive linear systems with bounded time-varying delays on time scales. For such systems on time scales, the positivity conditions are firstly established. Then, in virtue of the monotonic and asymptotic properties of a positive linear system with the specified time delay, the stability condition is presented for positive systems with bounded time-varying delays on time scales, which is independent of the delay magnitude and time scale. Furthermore, we prove that the L ∞ -gain of such systems is also independent of both the magnitude of delays and time scale, which can be fully determined by system matrices. Finally, two numerical examples are presented to show the validity of the obtained results.