On Observability of Hybrid Systems

Observability of a hybrid system is defined as the ability to determine the continuous state of the system. Whether a hybrid system is observable or not depends on which events can be disabled, which events can be forced, and the connectivity of the discrete states, as well as its continuous dynamics. We model a hybrid system using a hybrid machine that takes into consideration both continuous variables and discrete events. We classify hybrid systems into four classes based on their discrete-event parts. For each class, conditions are derived to check observability. If a hybrid system is not observable, then we check if a weaker version of observability, called B-observability, is satisfied. B-observability requires that a hybrid system become observable after some finite occurrences of events. Conditions are derived to check B-observability. These conditions involve both the discrete-event and continuous-variable parts of hybrid systems. If the continuous-variable part of a system has a constant A matrix, then the conditions for the continuous-variable part can be simplified. We illustrate the results by an example of a battery management system of an electric vehicle.