Stabilisation of discrete-time switched positive linear systems via time- and state-dependent switching laws

This study investigates the stabilisation problem of discrete-time switched positive linear systems by means of piecewise linear copositive Lyapunov functions. Two stabilisation strategies are designed under time- and state-dependent switching cases, respectively. The former case aims at determining an upper bound of the minimum dwell time to guarantee that the underlying system is stable for any switching signal with dwell time greater than this bound. The latter case is focused on deriving a state-dependent switching law stabilising the underlying system from the solution of a family of so-called linear copositive Lyapunov–Metzler inequalities. In each case, a sufficient stabilisation condition is given first, then based on which an associated guaranteed cost is further proposed. A practical system derived from the distributed power control in communication networks is given to illustrate the effectiveness and applicability of the theoretical results.