A Novel Event-Triggered Transmission Scheme and <formula formulatype="inline"><tex Notation="TeX">${\cal L}_{2}$</tex></formula> Control Co-Design for Sampled-Data Control Systems

This note is concerned with the event-triggered L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> control for a sampled-data control system. A novel event-triggered transmission scheme is first proposed to determine whether or not the sampled-data should be transmitted. Under this scheme, the sampled-data transmission should be executed only when a threshold is violated, which means that less sampled-data is transmitted. This scheme does not require any special hardware for continuous measurement. Then, the sampled-data control system is modeled as a sampled-data error dependent system. A stability criterion is derived by constructing a novel Lyapunov-Krasovskii functional which fully utilizes the sawtooth structure characteristic of an artificial delay. Based on this stability criterion, a sufficient condition on the existence of a state feedback controller is given. A co-design algorithm is provided to obtain the parameters of the event-triggered transmission scheme and the controller gain simultaneously. Finally, an inverted pendulum example is given to show the effectiveness of the event-triggered transmission scheme and the co-design algorithm.