On stabilizability of switched positive linear systems under state-dependent switching

This paper addresses the stabilization of switched positive linear systems by state-dependent switching. We show that if there is a Hurwitz convex (or linear) combination of the coefficient matrices, then the switched positive linear system can be exponentially stabilized by means of a single linear co-positive Lyapunov function. If there is not a stable combination of system matrices, it is shown that the exponential stabilizability is equivalent to a completeness condition on the coefficient matrices. When the switched positive systems can not be stabilized by the single Lyapunov function, we provide a unified criterion for piecewise exponential stabilizability in terms of multiple linear co-positive Lyapunov functions.