Stabilization of positive switched delay systems with a hysteresis switching law

This paper is concerned with the problem of stabilization for positive switched delay systems. A hysteresis switching law is designed to stabilize positive switched systems with a time delay. On one hand, such switching laws can eliminate the chattering resulting from state-dependent switching laws. On the other hand, a constant time delay may sometimes lead to the instability of positive switched systems. Sufficient conditions on the existence of hysteresis switching laws are presented by making use of linear programming approach. The validity of the proposed approaches is illustrated by a numerical example.