  We study the design problems of state observers and tracking controllers for
a class of hybrid systems whose state jumps. The idea is to utilize the
well-known method of gluing the jump set (a part of domain where the jumps take
place) onto its image, which converts the hybrid system into a continuous-time
system whose state does not jump. Sufficient conditions for this idea to be
implemented are listed and discussed with a few concrete examples. In
particular, we present a structural condition for an observer design, and, for
tracking control, we introduce a feedback to compensate residual discontinuity
in the vector field after gluing. The benefits of the proposed approach include
that the observer design does not require detection of the state jumps, and
that the tracking control does not require the plant state jumps when the
reference jumps.
