Integral-based event-triggered PD control for systems with network-induced delay using a quadratic generalised free-weighting matrix inequality

This study investigates event-triggered proportional-derivative (PD) control for systems with network-induced delay. Based on the Lyapunov-Krasovskii functional, the PD sampled-data controller design condition is derived in terms of linear matrix inequality (LMI) which include the integral-based event-triggering condition. As the derivative term of the proposed PD control may lead excessively frequent triggering, an integral-based triggering is firstly adopted to reduce the required sampled control input in this study. The proposed triggering condition with integration is converted as LMI with quadratic augmented vector by applying a new quadratic generalised free-weighting matrix inequality which provides a free selectable vector. Numerical simulation shows the effectiveness of the proposed event-triggered PD control with the integral-based eventtriggering condition.