ANALYSIS AND DESIGN OF DISCRETELY CONTROLLED SWITCHED POSITIVE SYSTEMS

Abstract

Discretely controlled switched positive systems are characterized by interacting continuous and discrete dynamics. Switching must take place not only to move the continuous state from the initial state to a goal state, but also to make the system remain in the surroundings of the goal state. The continuous dynamics are positive. This paper shows that if the continuous positive systems making up the switched system have a certain structure, it is possible to design stabilizing state-feedback controllers which ensure that the trajectories of the switched system cannot diverge to infinity regardless of the way the switching thresholds are selected. The trajectories of the discretely controlled switched positive systems can be restricted to invariant sets (called H-invariant sets) away from the equilibrium points of the continuous system parts. For a planar system, the trajectories within an H-invariant set converge to a stable and unique limit cycle regardless of the initial state. It is shown how this idea can be applied to design controllers which restrict the steady-state values of the continuous states to desired sets. Experimental results concern a manufacturing cell with hybrid dynamics.