Stabilization of continuous-time switched linear positive systems

In this paper we considered a few problems related to linear positive switched systems. First, we provide a result on state-feedback stabilization of autonomous linear positive switched systems through piecewise linear co-positive Lyapunov functions. This is accompanied by a side result on the existence of a switching law guaranteeing an upper bound to the optimal L₁ cost. Then, the induced L₁ guaranteed cost cost is tackled, through constrained piecewise linear co-positive Lyapunov functions. The optimal L₁ cost control is finally studied via Hamiltonian function analysis.