Further results on stability and stabilisation of switched positive systems

This study is concerned with stability and stabilisation of switched positive systems in both continuous- and discrete-time contexts. Several criteria of Metzler/Hurwitz and non-negative/Schur matrices are presented. By using these criteria and dual system theory, a sufficient condition for stability of switched positive systems is established. On the basis of the sufficient condition, a new controller design is proposed for switched positive systems. It is shown that the proposed design reduces the conservatism of the existing approaches in the literature where the controller gain matrices always have the property of being rank one. The results are also extended to discrete-time systems. Finally, two illustrative examples verify the validity of the theoretical findings.