Practical Absolute Stabilization of Lur'e Systems via Periodic Event-Triggered Feedback

Abstract

This paper deals with communication-aware absolute stabilization problems of Lur'e systems using intermittent state information. The full state information is sampled periodically, but transmitted over communication networks to the controller aperiodically according to an event-triggering strategy. The sequence of the event-triggering transmission instants is certainly a subset of that of the time-triggering sampling instants. Hence the time-triggering strategy prevents the event-triggering strategy from the so-called Zeno behavior immediately. We employ the emulation-based approach and divide the controller design procedure into two steps. First, we present a time-triggered controller guaranteeing the global exponential absolute stability for the resulting closed-loop Lur'e system. The obtained sufficient stability conditions involving the state feedback gain matrix and the constant sampling period are derived by means of absolute stability theory. Subsequently, its robustness is analyzed against the control input error induced by the event-triggering mechanism. Under a prescribed periodic event-triggering strategy with a freely selectable parameter, a periodic event-triggered controller is obtained for the Lur'e system to achieve practical exponential absolute stabilization. Finally, linear matrix inequality (LMI) techniques are used to compute all the control parameters.