Analysis and design of discretely controlled switched positive systems

Discretely controlled switched positive systems arecharacterized by interacting continuous and discrete dynamics.Switching must take place not only to move the continuous statefrom the initial state to a goal state, but also to maintain thesystem in the goal state. The continuous dynamics are positive.This paper shows that if the continuous positive systemsmaking up the switched system have a certain structure, it is possibleto design stabilizing state-feedback controllers which ensure thatthe trajectories of the switched system cannot diverge to infinityregardless of the way the switching thresholds are selected.It is shown that the trajectories of the discretely controlledswitched positive systems can be restricted to invariant sets awayfrom the equilibrium points of the constituent systems makingup the switched system. These invariant sets are known as H-invariantsets. For a planar system, the trajectories within an H-invariant setconverge to a stable and unique limit cycle regardless of the initialstate. It is shown how this idea can be applied to design controllerswhich restrict the steady-state values of the continuous states todesired sets. Experimental results concern a manufacturing cell with hybrid dynamics.