Event-triggered uniform ultimate bound control for linear systems with time-varying delay

This paper investigates an effective event-triggered control for linear systems with time-varying delay. For reducing the sampled data transmission amount, a novel event-trigger is proposed wherein a state-independent threshold is involved. For guaranteeing uniformly ultimately bounded stability, an event-triggered feedback control law is proposed. By aid of a new free-weight matrix technique, the event-trigger and control co-design method is conveniently obtained. By pre-specifying the threshold of the event-trigger, the event-triggered frequency and the ultimate state convergence region can be simultaneously regulated. In addition, the convergence rate of closed-loop system is pre-specifiable as well. More significantly, the minimal event-triggering time interval is given. During that time interval, the event-trigger can not be violated, thus the Zeno phenomena is excluded naturally. Numerical examples are provided to demonstrate the effectiveness of the proposed method.