  A reset controller plays a crucial role in designing hybrid systems. It
restricts the initial set and redefines the reset map associated with discrete
transitions, in order to guarantee the system to achieve its objective. Reset
controller synthesis, together with feedback controller synthesis and switching
logic controller synthesis, provides a correct-by-construction approach to
designing hybrid systems. However, time-delay is an inevitable factor in hybrid
systems, which can degrade control performance and render verification
certificates obtained by abstracting away time-delay invalid in practice. In
this paper, we investigate this issue in a practical manner by taking
time-delay into account. We propose an approach that reduces the synthesis of
reset controllers to the generation of reach-avoid sets for the hybrid system
under consideration, which can be efficiently solved using off-the-shell convex
optimization solvers.
