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.