A computation for reachability set in switched system with piecewise constant input

Switched system is a class of hybrid system drawing the attention in the field of control systems theory. Typically, the switched system consists of several subsystems switched according to a given switching law and can be widely seen in industries such as process control systems, temperature control systems and so on. From theoretical point of view, stability including switchings has been mainly analyzed and studied. Although various approaches for switched systems have been reported, few research about reachability with constraints has been reported. In this paper, we take a system in which inputs are constrained to a certain set, and study reachability for the system. Furthermore we propose a switching law based on partitioned states of the system and some computational algorithm for the switching law. Then the proposed method is applied to a simple numerical example.