Stability and guaranteed cost analysis of switched positive systems with mode‐dependent dwell time and sampling

Abstract

This study handles the issues of stability and guaranteed cost for switched positive systems based on a novel multiple linear copositive Lyapunov functions approach. Two different switching policies are devised. The first one relies on continuous time strategy and the other depends on the sampled-data strategy. The designed switching policies not only render the considered systems globally exponentially stable with a pre-specified adequate level of performance, but also decrease the switching frequency to rule out the Zeno behaviour. New stability conditions are presented in form of linear vector equality as well as linear vector inequalities, which can be readily solved by employing Linprog function. Moreover, based on the attained stability results, the authors further research an infinite time cost function. The effectiveness of the proposed methods is validated and illustrated via simulation results.