On Co-design of event trigger and quantizer for emulation based control

In this paper the inter-dependence of quantization and event-triggered control is investigated. We motivate the idea of co-designing the event-trigger and the quantizer for emulation based discrete-event control, and then propose a methodology for designing emulation based discrete-event controllers for asymptotic stabilization of general nonlinear systems. The proposed algorithm results in an easily implementable finite density logarithmic quantizer and a simple event-trigger. The resulting emulation based discrete-event controller semi-globally asymptotically stabilizes the origin of the system with a specified arbitrary compact region of attraction. The quantizer is designed to be endowed with hysteresis so as to avoid chattering of the controller. The proposed design is illustrated with a two-dimensional nonlinear system.