A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant is presented. The approach is based on the concept of Petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed-loop system, The synthesis technique is based on the concept of admissible constraints. An inadmissible constraint cannot be directly enforced on a plant because of the uncontrollability or unobservability of certain plant transitions. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissible ones, When multiple transformations of this kind occur, a technique is described for creating a modified Petri net controller that enforces the union of all of these control laws. The method is practical and computationally inexpensive in terms of size, design time, and implementation complexity.