EVENT-TRIGGERED DESIGN WITH GUARANTEED MINIMUM INTER-EVENT TIMES AND L p PERFORMANCE MOHSEN GHODRAT AND HORACIO J MARQUEZ * Abstract In an event-based scenario, the system decides when to update the ac- tuators based on a real time triggering condition on the measured signals. This condition can be defined in various forms and varies depending on the system properties and design problem. This paper proposes a framework to design the triggering condition while keeping Lp performance within desired limits. Our general framework captures several existing state- based triggering rules as a special case, and can achieve the performance objectives while reducing transmissions. Indeed, this general structure is shown to enlarge the minimum inter-event time by a specified amount, for a desired period of time. Numerical examples suggest that the proposed mechanism effectively enlarges the average sampling time. 1 Introduction It is nowadays well accepted that event-triggered control provides a competitive alternative to traditional time-triggered control ( [13,20]), offering performance very similar to classical controls while reducing the transmission of information between system components. Event triggered control was pioneered by [3] and has lead to extensive research including formal stability analysis ( [2, 10, 11, 18, 20]) and the references therein, and performance in its various forms ( [5–7, 12, 23, 25, 26]). Two important aspects of an event-triggered control are (i) the design should satisfy some form of closed-loop performance, and (ii) should guarantee that the execution times have enough separation to avoid excessive sampling. This sec- ond point is critical to any event design. Note that reducing communication between plant and controller is, in fact, the primary motivation behind event- based methods. However, since the execution times depend on the occurrence of a new event, the triggering rule has to be designed in a way to avoid exces- sive triggering, particularly the existence of an accumulation point in which an infinite number of events are generated in finite-time (also known as Zeno phe- nomenon). In this regard, most event-triggered laws define a threshold using the norm of a measured signal, typically, the state. Examples include [10,18,20,23]. Although this type of scheme has seen countless of successful applications and * The authors are with the Department of Electrical and Computer Engineering, Uni- versity of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: ghodrat@ualberta.ca; mar- quez@ece.ualberta.ca) 1 arXiv:1908.00260v1 [eess.SY] 1 Aug 2019