Finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance

Abstract

In this paper, the problem of finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance is studied for the first time. By exploiting an approach presented in positive systems which is different from the Lyapunov–Krasovskii functional technique, an explicit criterion is formulated for the existence of a special ball such that all the state trajectories of homogeneous nonlinear positive systems with degree 0<α<1 converge within it in finite time. We then extend the main result to the general nonlinear time variant systems. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results.