A Separation Principle for Linear Event-Triggered Output Feedback Systems

The purpose of this article is to revisit the well-known separation principle of classical control for systems implemented in an event-triggered fashion. We consider a scenario consistent of two independent digital channels for communications between a sensor and a controller, and a controller and an actuator, and propose a methodology to separately design controller and observer gains as well as the event conditions. Under the proposed design, we address the problem of restoring the classical separation principle for the event-based design. We show that fast enough sampling at the sensor-to-observer channel suffices to ensure a separation principle. In contrast, under fast sampling at the controller-to-actuator channel, a separation principle can be obtained provided that an additional mild assumption is imposed on the stability matrices. A numerical example is provided to support the theoretical findings.