This article introduces Periodically Controlled Hybrid Automata (PCHA) for modular specification of embedded
control systems. In a PCHA, control actions that change the control input to the plant occur roughly
periodically, while other actions that update the state of the controller may occur in the interim. Such actions
could model, for example, sensor updates and information received from higher-level planning modules that
change the set point of the controller. Based on periodicity and subtangential conditions, a new sufficient
condition for verifying invariant properties of PCHAs is presented. For PCHAs with polynomial continuous
vector fields, it is possible to check these conditions automatically using, for example, quantifier elimination
or sum of squares decomposition. We examine the feasibility of this automatic approach on a small example.
The proposed technique is also used to manually verify safety and progress properties of a fairly complex
planner-controller subsystem of an autonomous ground vehicle. Geometric properties of planner-generated
paths are derived which guarantee that such paths can be safely followed by the controller