Stability andL∞-gain analysis for a class of nonlinear positive systems with mixed delays
Jun Shen, Shun Chen · International Journal of Robust and Nonlinear Control · 2016
This paper addresses the asymptotic stability and L∞-gain analysis problem for a class of nonlinear positive systems with both unbounded discrete delays and distributed delays. With the assumption that the nonlinear function is strictly increasing, we first give a characterization on the positivity of the nonlinear system. Then, with some mild assumptions on the delays, a necessary and sufficient condition to ensure the asymptotic stability is presented. Moreover, an explicit expression of the L∞-gain of such nonlinear positive systems is given in terms of the system matrices. Finally, a numerical example is given to illustrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.