Stability and L1-gain analysis for switched positive systems: a mixed switching strategy

In this paper, we study stability and L1-gain problems for switched positive systems, in which stability for any subsystems do not necessarily requirement. First, the sufficient condition for exponential stability is established. By exploiting the multiple linear co-positive Lyapunov function method, stabilization and L1-gain conditions of switched positive systems are proposed. To reduce the switching frequency, a mixed switching strategy is proposed, which is different from traditional state-dependent or time-dependent switching. Then, a set of state-feedback controllers and a mixed switching strategy are dual developed to stabilize the system, and the corresponding linear vector inequalities are examined in terms of linear programming. Furthermore, L1-gain is studied as well. Finally, a numerical example is provided to show the validity of the proposed techniques.